yes and no. yes in that it'll reliably fire in most quality firearms and can kill men when called upon to perform. no in that it's a bit expensive these days, it has trouble actually stopping a determined attacker, and there are significantly better options available.
that being said, a Colt 1903, Beretta 1935, or CZ 70 have served as somewhat compact/slim backup pistols for over a century and work as intended. if you prefer to use a .32 ACP, i recommend sticking to 73gr semi-wadcutter above 1100 feet/sec (or near it) in a 4 inch barrel. you will have difficulty with consistent performance from hollow points, and ball ammunition will tend to tumble, which is nice, but often is anemic to actually stopping people with mal intent.
consider that modern 100gr lead wadcutters from a .380 ACP (or 9mm short) or equivalent (such as the 9mm Makarov) serve as police handguns in many countries, and question if .32 ACP is right for your situation. in small handguns it can be "snappy" though and are more "minute of man" and "across the room" pistols than anything else.