It depends on the male, most seem fine with having a female in the room, they can get a bit annoyed when she goes into heat but that's about it. There are some though that can get so worked up they can't even be in the same room as females.
There are a few other things to keep in mind though. One is that there is no guarantee they will get along not all chins like other chins, so even if you got him neutered and tried to bond them the neutering could have all been for nothing. Also neutering is a risky operation, a lot can go wrong before, during, and after, if you don't have a very experienced vet that knows chins there is a high risk of complications and death. It's not like a normal neuter since the testicles are held mostly internal, so it's more like a retained testicles neuter when they need to cut into the lower belly. Recover is long too, a few weeks to heal externally, up to 8 weeks for all the sperm to get out of the system (making it safe to start trying to bond the chins) and up to 12 week to fully heal internally, assuming no complications.
Another thing to keep in mind is before neutering they can have no playtime together, mating literately takes a split second, hop on hop off the deed is done. The cages also need to be at least 6 inches apart or they can mate through the bars. So you can't really bond them before neutering your male to even see if they get along, other then see how they react with their cages being in the same room.
Lastly, it's advised to keep any new chins in quarantine in a separate room from your current chin for 30 days when you first get them. This allows any illness to show itself before exposing your current chin, for you to book a wellness check with the vet for the new chin, as well as for the new chin to settle in, and for you to start building a bond with it.