Depends on the cause.

If it's because the "small fraction of men" is just really talented at getting dates, the effect would diminish, because they just don't have the time to be in ten times as many long-term committed relationships as anyone else.

But the same effect occurs, as an earlier post points out, in any subgroup in which there is a majority of men and a minority of women. Then, if all the women are out on a date, only a fraction of the men are, by virtue of the pigeonhole principle. In this case, I don't think anything changes if we look at longer-term relationships.