If I had a game on disc and I buy it from the Playstation Store, can I use the same data?

You might not like this answer, but if you didn't have a PSN account in April, you won't qualify for the freebies. If you have only just purchased your PS3, then this will be the case, and you should just keep the disc.

On the other hand, if you do qualify for the freebies, then yes--the games should share the data. I base this on the example of Dead Space: Extraction. I had the game on PSN before I purchased Dead Space 2 Collectors Edition, which came with a copy of the game on the disc. I installed Extraction from the disc, and then launched it from the disc--it shared the data from my previous PSN version of the game.

Of course, it could just be a special case with Extraction, but that would be quite unexpected.

The save files DO NOT work between blu ray version and PSN store version. I have tested this myself. You must start again from scratch.

I went ahead and downloaded inFamous, so to answer about my specific case: Yes, the disc uses the same save files as game downloaded from the PlayStation Store. Not even a tiny hiccup going between them.