The compatibility chart I use says yes, but it seems I have also read a bit about gouromis occasionally being aggresive/territorial. That would concern me a bit as to whether or not the angels would be turning up with pieces of fin missing. Let's see what some of the others have to say, but my opinion is that you are probably ok so long as you watch them for awhile to be sure they are tolerating each other.
It depends on the type of Gourami, some are more agressive, some are pretty peaceful (Dwarfs). Angels can be aggressive and territorial so I personally wouldn't do it, but other people might disagree
I think this is one of those 'outta work' things that probably will work but could end in removing fish to save them so a backup plan would be good. That being said.. Angels are cichlids, but probably the most peaceful of the cichlids from what I understand and if they're put in with fairly peaceful Gourami (the Dwarfs that Genie mentioned are probably the best gourami to try), your chances will improve big time to have a happy tank with beautiful fish that you can enjoy. Also, having a fair amount of hiding spots like rocks, plants, caves, etc. might help them in learning to co-exist with each other.
my golden gourami killed my angel in less then 3 weeks after I introduced the angel. if you mix them, provide hiding places.
I never had any Gouramis so I don't know their temperaments. But I have Angels. And Angels CAN be aggressive towards other fish, especially during breeding times. When an Angelfish pair is breeding ... it's best to stay away from them!
It sounds like a harder thing to accomplish than their data sheets would indicate. Sounds risky even with lots of hiding places.