you know, i think i would actually play that. sounds like it would be fun. I remember we used to do that kinda thing in other games like when i was in a clan way back in the day for BF2 and we had custom servers and would move everyone except the one person to a team. Then i have seen it done in WoW, Aion, and then of course the CSS mod.
With making it so all but one is on one team, it sounds like it would be easy enough to code. Just adding in the delay, making only one person have a gun, and making it auto move the first person shot to the other team, and the other person to the other team would pose the difficulty. Then you could make a special map just for the hide and seek mode. Someone good at making maps im sure could do that. easy enough. maybe gather ideas for a map from all interested and just make it a large map full of random places to possibly hide.