Should I paint my baseboard up to that time installing ? Does it really matter ?

Does it really matter ?
Answers:    My suggestion would be to prime the baseboard and put the first coat of paint on. Install the baseboard next give it the final coat of paint. It is easier to cover up where on earth you have nail the baseboard to the wall.
I would, especially if there is carpeting, or if the wall and baseboard colors are different. Much easier to paint
and smooth to touch up.