Of course!

The distortion channel, or stompbox, or whatever, has more gain than a clean channel. This means that any sound from your guitar gets amplified more, including the hum. I'm sure if you turned the 'clean' volume way up, you'd hear hum there, too. Of course if you accidently brush the strings while you're crouched in front of your amp, you may have trouble hearing much of anything for the next few days!

http://www.guitarnuts.com has very good advice about hum-proofing guitars. Or at least improving them.