Time Machine doesn't back up the contents of mounted drives for a few reasons. For example:
Mounted images can be very transient. If /Volumes/MyVolume exists on Monday but disappears on Tuesday, should it consider those files no longer existing and therefore remove from future backups? What if MyVolume comes back on Wednesday? Now it has to make a whole new copy of the contents again because it can't be sure the files are same ones it saw on Wednesday.
What if yesterday it's mounted as /Volumes/MyVolume but today it's mounted as /Volumes/OurVolume. Does Time Machine have to make a whole duplicate copy?
Backing up the contents of an image in addition to the image itself would waste space on your backup volume. You'd essentially be storing two copies of every file.
However, you can view past backups manually without taking the time to restore them. Browse to your Time Machine volume. For example, mine looks like this:
/Volumes/TimeMachine/Backups.backupdb/Hypatia/
2009-11-27-163215/
2009-12-11-075355/
....
2010-06-22-004524/
Hypatia/
Applications/
Developer/
Library/
System/
Users/
Rather than using the fancy Time Machine interface, if you are looking for a specific version of an image (or bundle) file, I suggest looking through those dated folders and mounting the backup copies of your image file directly. You can open the folder that contains the dated folders then use the window's Spotlight search to find every copy of the image you're looking for (i.e., search for "NameOfImage.sparsebundle").
This way, you save the step of copying it back to your system drive and overwriting whatever is there. It's a little more tedious than using Time Machine's goofy interface, but it gets the job done.
If the Mac still has the same name, the same hard drive and the same logic board, then Time Machine will not have any problems identifying it as the same machine again.
This means that your Time Machine backup will just continue to write to the already existing one. Of course, this results in a much larger initial backup since many system files need to be changed. The backup may take a very long time. But apart from that, the previous backups should be preserved.
If that's not the case, Time Machine will ask you for which drive to back up to and ultimately create a completely new backup. The old one will be preserved and accessible though – it won't be touched again.
It really depends on what you want to do. I personally would just keep the old backup archived somewhere and start a new one.
If your Mac continues to write to the old backup, note that old and unused files can be deleted from the volume. For example, at some point, Leopard's system files won't be used anymore and therefore removed from the backup. Your private documents though won't, if you're using them.
Nevertheless, Time Machine should work fine with older backups. In fact, there haven't been any (major) changes to Time Machine's file layout ever since it was introduced. However, it's not backwards compatible, therefore you can't use the backup on a machine with Snow Leopard or Leopard.
Best Answer
If worst comes to worst, you can just dig down the Time Machine drive hierarchy -
'Time Machine Drive' > Backups.backupdb > 'computer name' > Latest > then you get the same hierarchy as your backed up drives.
You can then just do a regular copy back to any other partition.
If Latest doesn't contain the files you need, then search could find them, or you could dig back down the dated backups