Heck no.
If they make 'allowances' in scoring for some disadvantaged group, it would only be fair to adjust scores for every possible contingency-- learning disabilities, physical disabilities, race, gender, socioeconomic status. Plus, that is not even taking into consideration the reason *why* these groups perform poorly. Socioeconomic status probably plays somewhat of a role in race, but not really in gender...that's probably more of a cultural thing. I don't know what groups fall short when SES is controlled for, but the fact is, the GRE is a test of how well you know English and basic math skills you will need in grad school (ok, it is a horrible test that seems like it doesn't test any of those things but that's another topic). When you level out the scores, the results become pretty meaningless, don't they? Granted, the GRE doesn't have a whole lot of ecological validity (they say scores are predictive of success, but so are many other things, and mostly people on the high end of the bell curve get accepted anyway)...but say someone's score is 'adjusted' from 570 to say, 610 based on the fact that they are from a group that tends to perform poorly (statistically, without even addressing whether the construct being controlled for is the one producing the variability). If the grad school does not know about this adjustment, they might assume they are getting someone better versed in statistics or the English language than they really are. Of course, interviews would reveal potential weaknesses, and this adjustment might result in schools accepting students for interview that would not have been considered (well, the score difference would probably not be that significant, but say it was). Good news for them, bad news for the applicant that might have gotten edged out. And this would create the whole affirmative action backlash of students resenting other students, feeling they got in based on subsidy rather than merit.
I am just opposed to the idea of two people who answered a set of questions identically ending up with different scores. There are numerous other portions of the application where a student who may perform below average on the GRE can explain these mitigating factors, and show that they are stellar performers in other areas. But your GRE scores, in my opinion, should reflect the number of questions you answered correctly, and nothing more.