Play PS2 data on remastered PS3 game
Solution 1:
Original PS2 and PS1 games running on the PS3 (this applies both to the disc versions and the downloadable versions from the PSN store) save and load to virtual memory cards on the system. If you use the adapter on your original memory cards, they'll transfer into these virtual cards and be usable by the original versions.
Remastered (i.e. HD) versions of PS2 games, however, use the PS3 save data format, and don't access the memory cards at all. So unfortunately, no, this won't work.