Yes and no.
First, in a case like this:
Go to Guild Wars Legacy, Reddit, and the official GW2 forum (same server as GW1) to see if you're the only one having this problem (or not). In the case of a few hours ago, there were numerous reports of this problem and an official response was posted.
And by the way, if you can connect to other sites and it's not due to the GW server, then the problem is more complex to solve than a simple general network error, so it's easier to go to the GW forums first.
So restarting your PC is not a priority. Otherwise, you can still restart your PC, see that it doesn't change anything, and check the forums or modem, etc.
Hey! I told you, I'm an expert. 
Edit: I feel like you were hurt by my negative thumb, so I put Dhumm's scythe in its place instead. Is that better? 