The Roku's XR is capable of using 802.11n. (as well as b/g) The router that comes with FiOS does NOT support 80211.n. (it supports only b/g) FYI: n is theoretically capable of much faster communication than b/g.
However: most b/g equipment is fully capable of supporting the bandwidth requirements of 720p (and lower) quality Roku bitstreams...
NOBODY can tell you for sure if wireless will work for you where you plan on setting up your equipment. Most of us that are serious about our communication still run wires for everything other than laptops... (It is nice to have the option of wireless because then you can run the wires when you feel like it instead of before you hook up the equipment. Also people who rent might be prevented from punching holes in the walls...)
Here is some info on getting a good WiFi signal. Your best bet for a guesstimate of if Roku will work wireless is to put a laptop right next to tv and see if you can connect to access point using it. (The limitations of Roku are likely to be similar)http://lmgtfy.com/?q=wifi+signal+strength