It is not likely to damage your revolver and it is, in my opinion, a better choice than .32 S&W Long. .32 S&W Long is going to sound and feel like a misfire compared to almost anything you know. It's going to be like one of those cork-guns that the kids in Cabela's are constantly popping off and for what you get in .32 S&W Long, it's horribly expensive.
The downside to using .32 Auto is that it's also a pipsqueak and the long jump from case to where it's headed doesn't do the accuracy any favors. But the bullet is the same diameter as your .327.
The best advice? Save up some pennies and seriously consider learning to handload. It will open up a new world and if you own a .327 Federal Mag, it's almost a necessity, much like it is for those of us who own, shoot and love 10mm. Handloading the .327 is fun, easy, and will drop your ammo costs so significantly, you'd hardly believe it. (however, let me duly note that there are absolutely some significant start up costs AND dropping the "cost" of your ammo requires making the largest bulk purchases you can make, so there really is no free lunch here)