Good question. Yes they do. fe: Not only does strength increase your melee damage, it increases your resistance to damage.
A follow up if I may:
Has anyone had success in increasing Special Ability level?
Yoga, headhots, and everything else suggested in Bradygames has yet to noticably icrease any of my protags SE.
Maxing special ability stat allows you to use it for longer , up to 30 seconds I believe .
For shooting ability use the range .
For strength you can play tennis , golf , Punch cows or punch people but this will draw the police to you.
For driving do continous wheelies on a motor cycle
Franklins special usually fills just by playing the game and driving
Special ability stat raises not by using the special but by filling the yellow special meter .
Michaels special can be raised by getting headshots during missions .
Trevors was the hardest till I realized all you have to do is fly around at top speed till the yellow meter fills , land plane or heli . Trigger your special , shoot into ground till yellow bar is empty and repeat .
Others are obvious ...
Lung capacity .. swim under water .
Stamina .. run around .
Flying .. fly .