Most 32-bit apps work on my system without any issues, so I would presume the only stumbling block here is the impulse client itself which refuses to restore the archive.
Actually, it should restore them regardless, but whether they work or not will depend on the application. Apps like WindowBlinds that need to have the 64 bit version on 64 bit systems will probably not work if the 32 bit version is installed, while apps like DesktopX may work fine.
Worse still, Stardock is not giving me any means to use my purchased product versions without a renewal, hardly a customer-friendly stance.
The products you subscribed to. Your subscription has expired. This is different than if you had purchased them outright.
I've never had Steam do that to me for any game I bought there so this is really quite disappointing and I feel little desire to renew my subscription with Stardock or recommend it to my friends for any software purchases.
Nor would you have the same issue with games purchased through Impulse as they are not a subscription. Nor with standalone applications. Your subscription has expired, therefor you do not have access to download or update the applications. Applications you have installed still will function just fine, and applications can be restored from archives as well. The issue here was your choice to switch platforms, which means that the archives you created on Windows XP 32 bit may or may not work on Windows 7 64 bit. If you have a machine that has Windows XP 32 bit on it, the archives should restore fine.