I wouldn't think you would since the repair is being performed on the host OS not the vhd. If you should run into problems running the VPC or VM ware, VBox program being used afterwards you would then need to redo the 32bit VM all over.
A good repair install generally aborbs just about all programs seen on the original installation with some exceptions at times for device drivers
mainly. The registry usually remains untouched while exporting and later importing a backup of that would have been one advice before the repair began.
Here I had previously installed Vista on a vhd for running that on the Virtual PC now no longer valid having restored a full system image to the drive some time later. That installation will have to redone due to that while you should stil be able to run the VM as usual once complete.
If anything goes wrong however you would likely see the 32bit VM simply fail to load up fully and stall on you leading to deletion of that for a totally fresh install on another new vhd. This is why the one big advantage the XP Mode sees over other VMs is the access to main drives in order to backup anything you have going on one. They can be fragile at times.
The best thing for now however is see how things go once the repair is complete. If the VM loads up normally you should be all set.