When Schrödinger was present in the SGC (season 3, when they dealt with the Tollan), the standard issue service weapon was still the MP5. The P90 was only introduced around the middle of season 4.
I don't think I can make fun of trekkies being obsessed with their trivia anymore.
Luckily p90s were issued before the Tollan were wiped out by Tanith.
So theoretically it's possible, but only technically. I got the feeling they didn't visit the SGC after they left except the two other times we see them. During O'Neill's "rebel" phase to expose Maybournes' off world shenanigans, and the very episode where they end.
I might be a bit of a Stargate nerd... And I can't even make fun if star trek nerds either because I'm one of those, too...
I feel that the whole point of the P90 is the small form factor and the full auto combined with a small fast projectile that is unlikely to over penetrate. Given the longer barrel and lack of full auto of the PS90 you might as well get a five seven for home defense if you want that Gucci factor.
I'm not any kinda fun person. But I did once get a chance to use an FN FiveSeven at a range once and it was fun. I was shocked at how much more I liked it over the 9mm's.