If the stealers (is that even a word? Tis now, bagsied it) bandwidth usage suddenly jumps, it could theoretically shunt the other people connected to it yes
I leave my mobile connected to my network whilst at home, but if I and my Gf both log into WoW, it disconnects the phone lol
Yes,I can see that especially if the OP is using an old Router especially with wireless B rather than G or the newer N type
or if it's not set up right (lacking passwords,encrypted etc.).
Myself I have a neighbor with a open router that I could use.I did use his router before for streaming Hulu videos for a while.Always encrypt your router's signals,use passwords,read the manual etc.If the router is of an older vulnerable type just ditch it and get a new one.