So the short answer to this is "maybe" or "sometimes". In my case, I think the Win7 Ultimate disc would have worked just fine.
It turns out that repairing a Win7 install can be more complex than just Pro/Ultimate/whatever. Apparently (http://www.sevenforums.com/tutorials/3413-repair-install.html), you have to pay attention to whether your install and repair disc both have SP1 (my guest does, my disc doesn't).
So I booted VM from the Ultimate disc and clicked through to the "Repair", "Cancel" or "view details" dialog (sorry, I didn't think to take a screenshot). The gist of the repair steps was that it wanted to repair the boot sector. Not wanting to take any risks, I cancelled out & shut down the VM.
I restarted the host and booted back into Windows 7 natively in order to burn a Recovery disc. After that, I restarted Linux, booted the VM from the recovery disc, and let it get to the same dialog as before. The repair steps looked the same as from the Ultimate disc - it wanted to repair the boot sector.
This time I clicked "Repair", and after letting the repair disc do its thing the VM rebooted itself, and things just started working! I can reboot into Windows natively or I can use VirtualBox, whatever I like.