This position may be a little stern, but once you are on the other side of the admissions table, you get bombarded with "Dear Professor, I am highly interested in working with you, do you have any positions available?" emails every week. A lot of these emails suffer from poor grammar, and most in fact miss the point of what I do, researchwise. As F'x said, if you decide to take the liberty of sending such an email, it (a) may be lost among dozens such emails, (b) may get you blacklisted by the department. (This is a very good school, and they will have no shortage of highly qualified applicants, and you hardly will be in a position of power in negotiating with them.)
Ideally, you would've established a contact with a faculty much earlier with something like "I believe there is a typo in the Appendix of your recent Biometrika paper" or "What R package did you use? I can't get lmer to work on a similar problem" or "I thought that M=5 imputations is always enough" or some other question relevant to both your studies/interest and their expertise. I've established a couple of the most long-lasting and satisfying professional relations by asking these curiosity-driven questions, even though I never worked with these specific researchers, in the end. Don't try to make this up, though, and make sure to produce something that will really pique enough of the professor's interest to reply.
As a faculty, I have been receiving meaningful emails, too, saying "You've published on this and that; I am working on the intersection of this-that right now as an analyst in Iranian government, but I realized that I don't know enough, and want to learn more..." -- to which I would have to say that the contacts between Iran and US are kept low profile. The fraction of such emails is low double digits, most are obvious academic spam.
Finally, the department may have similar language in the faculty bylaws discouraging faculty member from discussing financial matters and/or open positions with potential applicants. Basically, this would be done to avoid a mutually unpleasant situation in which a professor may promise an applicant the RA support, but either the applicant would not make it based, say, on their GRE scores, or the professor would not get that grant that they were expecting. The department cannot commit acceptance based on such side negotiations, so they want to minimize the risk of that happening. Likewise, a professor may not be able to promise to take you as an advisee if they expect to have five more students, currently in their second year, joining their lab to support the work on a new multi-million R01 grant. You will be taking the fundamental required courses for a year or two, and talking right now about what is going to happen three years down the road is basically waving a big question mark in the air.
So my bottom line is, if you want to talk about research, there is little to stop you; if you are told not to discuss the admissions process and the existing positions with anybody outside the admissions committee, don't.