Does the morale of the Capital has effect on the rest of the nation?

no according to official sources

if you will conquer capital then morale in enemy provinces will drop -20% while your provinces would get bonus +10%

additionally - without capital you get -40 points morale per day for not having a capital so I would advise to take capital ASAP.

you will also get half of the money El Presidente is hiding in a central reserve.

I see, thanks for the fast response!

5 k gold plzzzz