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Do we allow an asexual man to marry an asexual woman with the understanding that there will be no conjugal relations?*
And while we're at it: Does a woman have to go to mikve if her husband is home, but they plan to not touch each other?
*Maybe except for once to allow yichud during nidda.
Let's put aside questions of the obligation to have children. Most marriages have some unspoken assumptions, but if the couple goes in with this clear understanding, I really don't see the issue. Rambam writes "you may not marry a woman with plans to soon divorce her, unless she's aware of the plan and okay with it." Similarly there's a Gemara about a Kohen who married a woman (actually, several) simply to enable her to eat Terumah. If both sides go in to the marriage with eyes wide open, well, that's what it is.
As for mikvah, we generally recommend that a married woman stay as tahor as reasonably possible, but it's not an all-out requirement. (E.g. if he's on a three-week business trip, the kabbalistically-inclined will say she should wait to dunk until he's almost home; a more cut-and-dry halachist would say she certainly can dunk early if she would like to.) Here's a heartbreaking question to Yoatztot.org, a couple that's called it quits but won't officially divorce till the kids are married. It's recommended that she continue going to mikvah, but not required. Keep in mind there are other laws besides touching that come into play if she doesn't dunk, e.g. passing objects or even eating at a table for two! Assuming an asexual person still appreciates some sort of non-sexual physical contact (e.g. a back rub), going to mikvah is a good idea.
What's more, Chazon Ish's opinion is that (at least generally speaking) if a newlywed couple had time to consummate their marriage and didn't do so, and then she becomes a nida, the couple is not allowed to sleep alone in the same room -- even in separate beds -- whenever she's a nida, until they consummate their marriage. I don't know how that opinion would play out in situations like these. (Many other rabbis disagree on this point, e.g. Rabbi Ovadiah Yosef zt"l.)
