Our "main" archive server and SQL Server server are in a data center with the other replicated archive servers at their various locations. We've seen no issues.
We actually have been using virtual servers for years. Again no issues. One advantage is it is easy for IT to add hard drive storage.
Hosting a server is really just extending your network. The connection is the thing to worry about. Speed, latency and quality (packet loss and reliability).
You should perform some tests on your existing system. Pick a selection of light, medium and heavy assemblies and write down the time it takes to Get Latest/bring up Get latest dialog, View data card, Right click menu, Check out/bring up Check out dialog, make a small change, save, Check in/bring up Check in dialog. - The most common daily commands.
Then you will have something to compare with a new, or better if you get the opportunity, a test environment on the hosted system.