Don't you just hate it when software does that? It's happening more and more nowadays, both as an option (default on) when you download, or as an option (also default on) when you install. (If you download the one with the additional software option on, you don't get the option at install time. Quite sneaky really).
Anyway, if the software works nicely with the operating system it shouldn't cause any problems as such. At the moment I have two anti-virus packages installed - Avast (free) and Sophos (paid). I had been running Avast for ages (and still like it), but had a specific requirement to use Sophos for a job, and just never got round to cleaning them up.
I have not had any problems running the two AV programs at the same time.
The only issue it may cause is a slight slowdown as both systems check the same files.
It's still not a good idea though, and when I have fixed what I broke in Sophos I will be taking Avast off.