Sure, it is absolutely possible, and many users do that. All you have to do is make sure that you use a "prefix" with one/or both of you installations so you avoid any potential conflicts with table names.
I don't know of any significant advantages or disadvantages to doing this, though the following comes to mind:
1) Advantage - Back-ups might be easier as just backing up a single database backs up the data for both applications
2) Disadvantage - If the database goes down, both applications are impacted. With separate databases, this might could be avoided.
I don't know if the "oneclick" installer makes it easy for you to specify table prefixes at install time, so this might be an issue. Manual installs make adding the prefixes very easy to do.