I think it would definetly work. It could be used tactically, like, for example, when you notice your follower's HP is low, and you need to get over to him/her fast to open up the companion wheel and tell 'em to use a stimpak. Or you could use it to sprint to cover or retreat if your HP is low and you dont have healing supplies. Or it could be used simply get around. I've met my fair share of people who get a little ticked that they cant reach a certain point in a town in their desired speed (take Vegas, for example...freeside's two districts and Vegas's 3 or more districts). So this could definetly make things a bit easier while keeping to realism.
Another thing, though: If it is implemented, it should affect more things than speed. You shouldnt be able to shoot while sprinting, or, if you could, make it less accurate than a musket
. And, if using melee, there should be special momentum power attacks that do 3x damage and a possibility of knocking the opponent down, depending on your strength. And it should also be affected by armor...if your just wearing clothing, the speed will remain the same. if your wearing light armor, it shoul be a -10% Speed modifier. If youre wearing medium, mabye -35%. And, if wearing heavy, it should be -60% or -70%. Plus there should also be a negative modifier for weapons: one handed ones, like pistols or grenades, should have no negative modifier. Smaller two handed weapons, like rifles or shovels, should have -10%. And big weapons, like miniguns, fat men and super sledges, should have -20% or -25%. So sprinting would be more of a last resort for players who like to go into battle wearing power armor and use missles.