1) The manufacturer of the (bottom bracket) tool will not warranty it if you break it.

2) If you accidentally turn the impact driver the wrong way, you will likely destroy the tool/strip out the bottom bracket splines.

3) Trying to bust loose a stuck bottom bracket (especially if it is in an aluminum frame) has a good chance of toasting the threads in the frame. Use penetrant before attempting it, and realize that you'll likely need to chase the threads with a bottom bracket tap.

If you observe all the above, and are still okay with doing it, it can work just fine, though the tools themselves are not built for impact use.

For what it's worth, I found that an impact gun was a great expedient to working on bikes that lived hard lives, but it was rough on the tools. You risk damaging parts, especially if they are stuck, but for removing square taper cranks in good condition, a 'universal puller' with a long impact socket is the fastest. Use on expensive cranks at your own risk--I only used it to remove for disposal...

I maintained a 2 foot, 1/2" breaker bar for stubborn parts on a bike. If you wind up needing more than that, there's a good chance you'll damage something removing the part. A helper should hold down the bike on the ground (wheels on!), while you apply steady pressure. You may need a large socket to fit over the removal tool, especially for a bottom bracket; these are sold as impact sockets at auto parts stores, individually, for use on hub nuts. A 600 foot-pound gun simply may not have enough oomph for a stuck bottom bracket, given the size of the threading.