Yes. That type of bullet is very popular in cowboy action shooting because it feeds very well in lever action rifles. Lots of cowboy shooters use lighter than "standard" bullets; in .38 Special for example I use 105 and 125 grain bullets.
SASS rules mandate that the ammo be loaded with lead bullets at no more than 1000 feet per second (for pistol ammo; the rifles are pistol caliber but the velocity limit for rifle is a little higher). This is because cowboys shoot steel targets at relatively closed distances and a lead bullet at the proper velocity (there is a minimum limit as well) tends to splatter and fall to the ground instead of bouncing off the target.
Look on the Hodgdon powder website; their printed manual has an entire section dedicated to cowboy action loads and I believe the online "Reloading Data Center" has the same data for lead bullet loads although they are not specifically identified as "cowboy loads".
I have used my "cowboy" .38 Special loads for practice ammo in double action revolvers. It doesn't cause a tear in space-time or anything.