A criticism often laid against 12 step recovery is that it is too God-centred  or religious-based in their program orientation?

Something I personally have not experienced in the years I have attended AA, NA and Al Anon.

Are there any studies on this either way, to shed so light on this persistent (perhaps distorted) perception of 12 step recovery?

This study (1) seems to support my experience that 12 step recovery is inherently spirituality based and not religious based.

It is a study conducted on Narcotics Anonymous rather than AA which makes a refreshing change.

“NA owes its origins, in the 1940s, to an attempt by opioid-addicted inmates in the United States Public Health Service Hospital in Lexington, Ky, to adapt the AA’s format for narcotic dependence.

NA World Services Office now reports that there are more than 58,000 NA meetings in 6 continents (Narcotics Anonymous, 2010). Because of this sizeable membership, an understanding of the nature of remission from drug dependence in this fellowship can shed light on one notable way in which a spiritually grounded recovery can be achieved.

…respondents report on average 6.1 years of continuous abstinence that began, on average, more than 5 years after their first attendance at an NA or AA meeting. This suggests that the process whereby NA engages people to achieve full abstinence may take place
only after a protracted period of time after first Twelve-Step
encounter, possibly punctuated by periods of relapse, until the cognitive, social, and spiritual elements of the program achieve full effectiveness.

The relative role of spiritual experience in the Twelve-Step recovery process has been investigated from various perspectives, generally in relation to patients’ experience in AA. Kelly et al. (2009) found little support for a role of AA’s specific spiritual mechanisms.

In fact, with regard to religiosity, Tonigan et al. (2002) found that, although atheists were less likely to attend AA meetings, those who did join derived equal benefit as did spiritually focused individuals.

On the contrary, in one study on persons recovering from cocaine dependence (Flynn et al., 2003), respondents attributed their positive outcomes to religion and spirituality.

In addition, Zemore (2007) followed up a large sample of substance abusers 1 year after inpatient treatment and found that the increases
in spirituality contributed to the increments in total abstinence
associated with the Twelve-Step involvement.

The NA’s theistic orientation is compatible with that of the general American population, because, according to Gallup (2012) polling, more than 90% of a probability sample of [AQ11] Americans endorses believing in “God or a Universal Spirit.”
Our respondents demonstrate a strong commitment in scores
on the NA beliefs. They more often designated themselves as
spiritual (93%) rather than religious (31%), and only 25% of
the respondents reported going to church at least once a month.

The finding that the NA members attend church relatively
infrequently may merit further examination.

These responses stand in contrast to the probability samples of the general US population, who more often designated themselves as religious (64% vs 31%) and less often as spiritual (79% vs 93%) and were more likely (73% vs 25%) to attend church at least once monthly (Adler, 2005; Davis, 2009).

On the contrary, 71% of our respondents reported that they feel God’s presence most days or more, compared with 57% in a
community sample (Kosmin and Keysar, 2009). The orientation
of the members toward spiritual experience rather than religious practice as such is reflected in the findings on the variables “feeling God’s presence daily” and current church attendance.

Only the former variable was significantly correlated with a greater duration of abstinence, the number of also associated with the less craving and lower depression scores, all underlining the importance of the concept of God or Higher Power in the Twelve-Step model.

Spiritual Awakening

One issue that we examined was whether the respondents reported having experienced a spiritual awakening.

The 12th step of the NA begins with the phrase “Having had a spiritual awakening,” and this experience, although described by NA members in different ways, is thought by many members to be a key element in their long-term recovery.

In one study (Matzger et al., 2005), alcoholic persons indicated that their positive drinking outcome was attributable, at least in part, to
a spiritual awakening.

Perhaps most telling is the finding of Kaskutas et al. (2005) that alcoholics in a treatment follow-up who reported a spiritual awakening were more than 3 times as likely to report an abstinence outcome than those who did not.
Importantly, among our sample, 89% of those who reported a
spiritual awakening reported that it made abstinence easier for them. This suggests that, at least for longer-term, established NA members, spiritual experience is an integral part of their membership, even if they may be less religiously oriented than other community members.

Spirituality among long-term members is likely instrumental in sustaining the integrity of the fellowship itself.

The prominence of spiritually committed long-term members at
meetings and their availability to serve in the sponsorship role create readily available models for earnestly held sobriety.
They serve as role models for believing commitment to the Twelve-Step spiritual ethos to help newcomers achieve stabilization in membership.

Sponsorship
The NA publishes a monograph on sponsorship with guidelines and examples for both sponsors and sponsees (Narcotics Anonymous, 2004), reflecting its role that a sizable number of long-term members have in transmitting the culture of the fellowship. Sponsorship embodies the fellowship’s altruistic orientation, reflecting a “helping and helper  therapy principle” (Pagano et al. 2011). Sponsorship apparently plays an important role in the recovery process for these respondents, given the high prevalence of having a sponsor and serving as a sponsor, as do other aspects of social affiliation with members.

High sponsor involvement over time has been found to predict better abstinence over long-term membership  (Witbrodt et al., 2012).

It may as well be that, although social support is key to early engagement in the Twelve-Step membership, over time, spiritual issues emerge as increasingly important in the members’ Twelve-Step based recovery.”

References

1. Galanter, M., Dermatis, H., Post, S., & Sampson, C. (2013). Spirituality-based recovery from drug addiction in the twelve-step fellowship of narcotics anonymous. Journal of addiction medicine, 7(3), 189-195.