Yep. I've dispatched several times with no working AP or AT in a 737. Also done it in ATPs BAe146 and Q400. Not an issue. The 737 was while working in Turkey so Non RVSM and it was a domestic, though a longish one. Both F/O (Ex Turkish Army Helo pilot) and I had no issues and did both climb to TOC and part of the cruise and handed over to setup and brief then took back control.
Back in the UK I've also taken an aircraft with no AT, but that was a hand me down to prevent a delay as several other crews had rejected it. MAINTROL were pleasantly surprised! The F/O was quite nervous though, till we were on the way and he realised it was a non event. I guess we get into a comfort zone and don't want to do any work here in the Western world......