If your speaker isn't properly secured, it will work, but it will rattle like a lot and sound just awful. That's one of the problem with those cheap speaker adapters, fitment usually leave a lot to be desired. If you want a nice permanent solution, I make custom speaker adapters for most Nissans with 6.5" speakers, but I have yet to make an S13 adapter. Here's the ones I made for my car:
They are made of PVC so they won't warp or crack. I've considered making sets for S13s, but I wasn't sure if there is much of a market left for them. Shoot me a PM if you're interested in having a set made. Good luck!