does time machine back up open dmg files?

I use password-protected dmg files for various directories on my mac-mini.

My understanding is that creating a dmg (disk image) with password protection actually

encrypts the contents.

When I open the disk image, it appears as an 'external disk' would on my desktop.

I can then access the directories and files easily, without the need to password

protect each one individually.

I have a question regarding time machine:

If the dmg file is 'open on my desktop' while time machine

does a back-up, does the unencrypted content get backed up?

I know that the files.dmg file itself gets backed up by time machine,

but that is password protected and encrypted.

My concern is that time machine would (against my wishes) make

a back up of the unencrypted/unprotected content.

== Allen Gorin