No. I wouldn't do it for a few reasons.
1. Betta and gourami are in the same family, both are territorial and do not tolerate each other in their territories. Males even more so.
2. Bettas do best over 80F and most gourami species do better below 78F. So theyre not temperature compatible.
3. A 20 long isnt the most spacious for territorial fish, so if it was even attempted, i would opt for 55g or larger. My gourami is still a butthead in my entire 46g, he would have a field day terrorizing a betta in it.
If you want a gourami, you could get a second tank. If you arent fussy on species, get a 10 gallon and get a trio of sparkling gourami