I think it's more about whether it is a free vote. Something that is a free vote is usually a free vote because it is a matter of conscience. I think that is the case with that bill. Most bills are not, so I don't think it would come up very often.
However, I do see that as a big problem with your schedule. You have two break weeks between now and the time when that bill is supposed to be passed, according to the Supreme Court. The number of members who will be able to speak is going to be limited by that, and maybe further limited by time allocation.