I think that there is a role gender-as-social-construct plays, Lass, though you're right it's not as simple as "society moulds them into sex attackers." It's more that gender-as-social-construct provides a certain type of man with a set of off-the-shelf excuses for his behaviour, excuses which society at large buy into far too readily (at its most pernicious in the form of the attitudes of people prosecuting rapes, or failing to prosecute them, and judges and juries).
If you look, for example, at the work of David Lisak (American psychologist who studies date rape), something round 6% of men on American campuses will admit to behaviours which meet the legal definition of rape. That's a lot of men. And these are (presumably) the demographic who are fairly privileged in terms of income, educational opportunities and job prospects. (Relevant for reasons I hope I can make apparent). They hide behind what Solid Gold Brass calls the good-guy-rapist persona. The idea being that what they think what they do isn't rape, it's just fairly insistent seduction, or being a jack the lad who takes the golden opportunity a woman's drunkness provides, or (insert other self-serving excuse here). And I think gender stereotypes do play into this.
Rember gender-as-social-construct isn't an exhaustive, internally consistent set of rules. It's a loose set of overlapping social norms, some of which actually contradict each other (the Daily Mail is a great example of this in action - they can villify benefit scrounging mums on one page and working mothers on the facing page without worrying at all about this!) And it's about far more than simply dress, or makeup, or shaving or... It's about "appropriate roles" in the sense of jobs, and "appropriate spaces" (working mens' clubs, pubs, dark alleys, car repair shops etc... all those places where traditionally a woman entering them would often find herself feeling very uncomfortable in). And about sexual double standards in behaviour (one example - the film Better than Sex has a flag on the IMDB site for "female promiscuity" - despite the fact that in the film the male protagonist has actually had more sexual partners).
So when someone says "gender-as-social construct" plays a role in contributing to a rape culture, they don't mean "women with shaved legs are more likely to be raped", or that "bringing boys up to play with guns and be inarticulate about their feelings turns them into rapists". That would indeed be ridiculous. But at the same time, I'd argue that some of the gender norms society constructs around appropriate female behaviour (nice girls don't ... have sex, get drunk, whatever, and girls who aren't nice are fair game and have brought it on themselves) do contribute in a very real sense to the set of beliefs that enable the "good-guy-rapist" to continue in his behaviour patterns (and Lisak also notes that these are not one-off offenders, these are serial, repeat offenders, with an average of 7 offences to their names).
And, I think more importantly (because I don't suppose these men would stop if you could somehow make it clear to them what they were doing, they'd just find an alternative set of justifications), they play into society's expectations about what's right in the way of responses to victims, how likely convictions are to be obtained.