Getting a clean number is one potential issue. If you do decide to go with Google voice, make sure you do a search for the number first and make sure it wasn't associated with another business (or anything else) in the past. It'd be a good idea to get it live and point it to your phone for a week or two and see what the junk call volume is like, some numbers come pretty dirty. It's not a bad idea to use a proper tracking number though, if you're going to go that route.
Callrail has some good tools for local businesses I know, though I haven't used them. (been a long time since I've worked with call tracking). Whatever you use, you're going to have to use it everywhere (treat it as a real phone number) but it can still be helpful to track what business came from the new location.
Why are they sending all calls to a central location though? There aren't a lot of circumstances where that's warranted. It's explicitly discouraged in
Google's Guidelines:
Use a local phone number instead of central, call center helpline number whenever possible.