I was looking at the Harbor Freight Medium Impact Air Hammar, (Air Hammar), but I'm not sure if it's a good match for my 6 gallon pancake compressor. I'm not looking to use it for very long, more for occasional DIY stuff, but I don't know if it can be run off of it. Would there be any obvious problems with this set up?
You don't mention the model of compressor, but virtually all can produce the 90 PSI pressure. The main issue with air impact tools is that they use a lot of air volume. That tool is listed as average air consumption of 4 CFM. "Average" means use of typical burst duration and frequency--how long you actively operate the tool and how long it rests allowing the compressor to refill.
If your compressor can provide 4 CFM at 90 PSI, you can use the tool in a typical way. If the compressor can't provide that volume, you would be limited in how long you could power the tool before giving the compressor time to refill. If your application is light, intermittent duty, it might not be an issue. But below some compressor capacity, it might become impractical. You would get a short period of use, then have to wait for the compressor to refill.
I've used a small air hammer similar to that with a small compressor. It was fine for intermittent use. But I once tried to bust up a concrete footer with it (ridiculously wrong tool for the job). A jackhammer would have made short work of it, but the hand tool required almost continuous hammering over a very long period. I spent more time waiting for the compressor to refill than actually getting work done. So you need to apply some common sense and reasonable expectations.