I think they would get along fine. It always depends on the individual though...some Bettas will tolerate absolutely nothing with them. You should always have a back up plan just in case. But I don't see why they shouldn't get along. Just make sure the tank is plenty big enough for them. UDC's get almost 4 inches and need to be kept in groups of at least 3, which is 12 inches right there.
I have to warn you about this: Upside Down catfish are very shy unless you've got at least three of them. I barely know mine exists. When I have cleaned the tank a bit he sometimes is seen startled, dashing to another hiding place. He ONLY comes out at night. That may be him as an individual but really I'd almost rather I hadn't got him.
Also Omorrokh is perfectly right: bettas can be very territorial and ornery. Not all bettas--some on here will tell you that they have happily kept bettas in community tanks. My betta hated any tankmate and would hound them to death.