can't see your other question - so based on this one
It's possible - but not for the reasons you give
wireless routers are affected by lots of external things
microwave, fridges, thick walls (and floors), rain, the coils used in TVs "noisy" power units next door's router .... blah blah (just about everything affects them)
(your monitor could also physically reduce the signal strength by being in the way).
and finally
your machine could be slowed down by the monitor (indirectly) if the resolution and colour depth is set too high
http://www.thescreamonline.com/technology/moni tor/monitor_res.html
the machine's graphics will struggle to keep up