It can. It usually doesn't. I have a 4' 60 gal tank that has housed an orange skunk pair and a percula pair for at least 5 years. Both of the pairs spawn regularly. The percs lay about every 10-14 days. The skunks spawn less often, but spawned sporadically when they were by themselves as well. There have been many times when both pairs have had eggs at the same time. I have never seen any conflict.
I believe this to be the exception rather than the norm. Personalities of clowns will vary, even within the same species. I think there are some reasons it has worked for me, but I also got lucky that I don't have any nasty females.