Suspending a line means there is no longer access to VzW's network until the suspension is removed. If the phone is capable of accessing wi-fi, then it can still gain access to the internet, access apps, etc.
Yes the wifi on the phone will still work. My son, who is deployed, has his line suspended on our account but he uses Viber to connect with us via text, video, or calling by using the wifi on his phone. It is similar to Skype but no cost for calls. FYI, military can have line suspended for longer than the 3 month normal suspension but you have to talk to a rep to do it.