Parallels is a program like any other. You create virtual hard drives on your current hard drive that it uses to store the Windows installation. It is just like creating a disk image on your hard drive. To the computer, it looks and acts like a hard drive, but it is cut out of space on your hard drive. To your Mac, it is just a single file.
Search the internet for "virtualization." Or, look on the Parallels/VM Ware websites for how it all works.
Because the OS sees the Virtual Disk as a single file, if you go into Windows and add a transaction, that whole file changed, not just the single transaction.
Time Machine* "listens" for changes in files. When it detects that a file changed, it backs up the entire file. It doesn't go in and back up the part of the file that changed.
If you could break that virtual disk image into tiny slices, then Time Machine would only see one of the tiny slices change instead of the entire virtual disk. Apple uses that concept in what it calls a Sparse Bundle Disk Image. Database systems use the same method. The "slices" are called stripes. So, to be Time Machine-aware, the developers would have to store large amounts of data in a sparse bundle disk image so that Time Machine only sees when one of the stripes changes and just backs up that stripe.
I don't know whether Parallels or VMWare use Sparse Bundles for their virtual disks. If they do, then you could back them up efficiently with Time Machine. If they don't, it would be better to use something like Carbon Copy Cloner to just back up the Virtual Disk Image periodically (it can be scheduled).
It is a combination of both. To make Time Machine fast, it doesn't look inside each file to determine what has changed. It just looks to see if the file changed, and then it backs up the whole file. Because of that, software engineers need to take advantage of Sparse Bundles if they intend to store large amounts of data the user might want to back up. I don't know what the tradeoffs are in using a Sparse Bundle vs writing straight to disk.
*It is actually a process called fsevents (file system events) that watches and logs every change to the file system. Time Machine uses that database to determine what needs to be backed up.
P.S. You seem fixated on Parallels. There are two other options, VMWare and VirtualBox. For what you need to use Windows for, I would use VirtualBox. It is free and will work just fine. They have done a very good job keeping up with OS X updates and upgrades.
For any of them, you will need a copy of Windows to install on the Virtual Machine.
