Even conquest players are likely to consider this issue in this GOTM (deity and the need to attain Frigates or Ironclads.) Here are my thoughts on the subject:
In republic every citizen earns one more arrow. You have to pay support for at least 2 units (a defender and a ship), and passify 2 more citizens (assuming that in Monarchy you would keep 2 defenders and one boat). Thus the cost of the republic is 2 shields and 4 coins. At 2.5 coins per shield the cost is 9. The advantage of republic is one extra arrow per citizen. Thus the breakeven point is when your city is size 8. This takes quite a while.
The above ignores two things. One is that with a marketplace each arrow turns into 1.5 coins (you also incur a cost of 1 coin) and thus the breakeven point is city of size 6 (you actually get an advantage of .5 coins here). This can be attained much earlier but still not early enough to justify skipping Monarchy.
The other thing being ignored here is trade. Those extra arrows turn into bigger payoffs from trade.
My conclusion is that early republic here is not justfied before trade. And since early trade requires Lighthouse I doubt if one can trade early enough to justify early republic.
