Yes it will help. To avoid raising the action to avoid fret buzz you will also need to be more gentle with the plucking hand. This will therefore help that hand too.
A problem with traditional sets is due to tradition and their naming people think of 45-105 as 'medium tension', it isn't, it's actually a very high tension, unnecessarily so, bass guitar only needs 30 pounds of tension.
Problem is bass guitar still thinks it's an electric contrabass, with a corresponding high tension. Hopefully things will change for more playability and to not put off people from playing bass, you should not need a vice-like grip.
I've noticed that bassists seem to often have injury, and it's not surprising considering the string tension and poor instrument ergonomics of almost all basses.
Looking at the tensions [This invalid link has been removed] the top 2 strings are tighter, when in fact higher strings don't need as much tension as the lower. There is a more balanced feel and playability with tension falling slightly from low to high, so i recommend 95 70 50 35 in singles.
Also, keep your wrists fairly straight, play sitting down to bring the nut closer, basses are very unergonomic when strapped-on, they are shifted too far to the left.