I would think the only reason not to use it for other things would be hardware or software conflicts. The potential to pick up a computer virus. Most are going to surf with the same computer anyhow, so the same protections apply.
There really shouldn't be any software conflicts if you closed one program before launching another intensive application.Even with multiple programs running, it usually isn't a problem other than the cpu taking more of a hit.
So no, I see no reason not to utilize those resources for other things. I would save my files though, just in case you have a problem. Nothing like working for days on a mix and then loosing it.
Hardware won't give you a notice before it fails. That can happen to a dedicated machine too.
I'm mostly away and do much of my email and social stuff on portable devices. Only use music computer occasionally for that stuff.
We have a few here who won't ever use their music computer online. It just never happened that way for me.