A-ha. I may have misunderstood the question; I thought we were referring to periodic APU starts. I believe we need more information on the equipage and certification of the airplane. Looking through my handy 737 NG FCOM, I don't see any evidence of a RAT, which is interesting (I am not typed on the airplane), but then the device most of you are referring to is the HDG (or HMG, depending on who wrote your manuals), which is the hydraulically driven generator. That is the ETOPS backup which automatically picks up critical services if both main generators fail. The RAT, at least on the 767 and 757, only provides basic hydraulics for flight controls.
If the question refers to continuous operation of the APU during ETOPS, that is interesting...there are 757s that are not equipped with the HDG and thus not ETOPS capable, and then there are those that are equipped with the HDG and thus (with other additions as well) are ETOPS capable. What is interesting to me is that the 737 NG could be ETOPS capable without the HDG or similar device, as I can't see my current employer failing to utilize non-HDG equipped 757s on ETOPS if there were a way to do it...
Of course, if you blast off into subspace with one generator inoperative, then the APU has to be running whether ETOPS or not.