Mind you, so called "12V lead-acid" fully charged battery has ≈13.8V voltage, so if you connect something to the car power system allow for that margin ..
In most cases alternators are three-phase generators equipped with three-phase rectifiers; the output voltage is not "pure" dc, but has ripples (see picture below).
A battery can be treated as almost ideal voltage sources, so its internal resistance (impedance) is close to zero; if a voltage with ripples is connected to a battery the ripples will be "smoothed" by the battery and the voltage at the battery pins will be, or should be, pure dc ..
Connecting an alternator (with rectifier) to battery means that current flows to battery at the peaks of ripples and is taken from battery in between .. Obviously, the former has to be higher than the latter, and therefore battery will remain its charge ..
Regards,
IanP