If you add a winch plate that ties into the frame, I don't see a problem. The bumper isn't as strong as some aftermarket bumpers and won't offer as much protection, but as far as the winch goes, should be okay.
The winch bolts to the winch plate, which bolts to the frame. The stock bumper has no impact on the strength of the winch attachment. Whether or not it looks good is up to you. Many after market bumpers have an integrated winch plate, which can look cleaner.
FWIF – I’ve stuck with the stock front bumper (and cheap winch plate) because most after market bumpers 1) add significant weight, and 2) protrude about 2” further than stock (reducing your approach angle). The Savvy bumper is the only one I know of that doesn’t have those two problems.