I sincerely doubt if it's recessed.
S&W didn't start recessing cylinders on their revolvers until 1935, when the .357 Magnum was introduced.
This gun is likely a product of the 1920s, when the vast majority of these were made.
It could be later, but I'd still doubt if it were recessed. That was pretty expensive, and only a few thousand .357 Mags. were made, and few made it out of the country, by the time production was suspended for WW II.
As for whether it should be shot or not?
Quite frankly, I'd have to say ARE YOU OUT OF YOUR MIND?
There is only one way that I would ever shoot this thing...
With blackpowder handloads, lead bullets, and a long, long string.
I have a funny feeling that even a moderately powered .38 Spl. load would do serious damage to it, and given the sheet corrosion on the muzzle, I wouldn't be at all surprised to see the barrel split.