Can/Should I put iTunes files on a separate drive?

A look at my storage situation shows that iTunes files are taking up a pretty big share of disk space. I'm wondering if I can or should put iTunes and its files on an external hard drive, which would give my iMac some breathing room.

Will that interfere with Time Machine, backups?

Will it make the music inaccessible when I want to listen via my iPhone? (As it is it's pretty dodgy now. Sometimes it works, sometimes not.)

Has anyone tried this or know that this is something I shouldn't do?

Any insight would be greatly appreciated.