Three problems with getting the free tech in the MA and not republic:
1) You get republic later, so your civ is bigger so your anarchy is longer
2) your research on republic is slower - less commerce and more corruption
3) You can't get cities to grow with irrigated grass until later.
For this to make sense, you'd have to be able to research republic in despotism faster than you would research, say, Education in republic. Education is a little more than 50% more expensive than republic, republic should give about 50% more commerce and on warlord, you'll get 3 to say 5 or 6 citizens before riots (3 free plus assume 3 or so native luxes)
With the ability to grow faster with irrigation in republic, I think taking republic is the better move - but it's closer than I would have expected.