Is it normal for a car with no overflow to dump a bit of antifreeze after a day

Common practice is to fill the radiator to within 1-inch of the top of the tank to allow for fluid expansion when hot.
Fill it more than that and it will probably puke some out until it's 'happy'. Your overflow/catch bottle will solve the problem.
A 'closed' system will also allow the engine to run a little hotter without boiling.