Not really, no. Adobe Digital Editions stores the decryption info in the registry.
You will have to sign in again with the same Adobe ID you used on the old computer.
Note: Once you do that, you can also just re-download all your books from the store you purchased them from.
But as long as you are registered with the same Adobe ID, the backed-up copies of the books should also work.
...
Personally, I find it much easier to DeDRM with Apprentice Alf's tools:
https://apprenticealf.wordpress.com
Then I don't have to worry about books getting lost.
