It surely should!
The .32 H&R Magnum cartridge is no more intense than a .38 S&W Special +P. The gas erosion factors should be about the same with both of these cartridges.
For entertainment purposes, (read: informal target practice, small game hunting, pest routing, etc.) you would be more than amply served by a nice spicy .32 S&W Long load in the revolver, or a light load in the .32 H&R Magnum case. (This is recommended only if you do not vigorously clean the revolver's chambers with a .32 caliber stainless steel brush.)
The .32 S&W Long is a delightful cartridge in ANY revolver in which it can be fired. Supremely accurate, and more fun than the proverbial "barrel of monkeys" the .32 Long is NOT a "magnum" cartridge, so it tends to get lost in the dust of its siblings.
Take it from me, it can be a real small-game getter, "pest eliminator" and all-around general purpose target-round and "plinker." It was employed, quite successfully I might add, as a police matron's cartridge in the NYC department for more than 50 years. It was seen in the .32 S&W Hand Ejector, Colt's Police Positive, Colts Detective Special, Colt's Pocket Positive, S&W's Regulation Police and many other brands (H&R, Iver Johnson, Hopkins Allen, and more.)
Don't sell the little .32 short. It has stood the test of time for well over 100 years. The .32 H&R Magnum was simply a logical outgrowth of "the world's most accurate revolver cartridge." Ask any target shooter from the 1950's they'll tell you!
Scott