12v car power supply with 160a alternator and 30a relay, will this system support upsizing the cooling fan from 7a to 20a?
If you have a typical old school Hot Rod it should be more than enough. Most cars from the 60's and early 70's used alternators that only had an output of 50-75 amps. If you have a large high powered amplifier or some other high load device you have to calculate for that. I don't understand the reference to a 30 amp relay.
As @mikes stated that this depend on the amount of power which is already being drawn on the system. That said, 160A alternator is a fairly large alternator. If you don't have a lot of other things on the system, there should be no issue with the power draw itself. Your amp draw is only going up by 13A at peak draw. A 30A relay is more than enough to handle a 20A fan, so there should be no issue there either. The one thing you really need to look at here is whether the fan itself is going to draw enough air to cool what you need cooled. Other things to consider is the size of the radiator itself.