Yes...Kind of.
The system has two sides .The Low side [evaporator] and the high side
[ condenser] . The main cause of high side pressure is the output of the compressor...but the proper refrigerant level effects this capacity.. the compressor can not compress something that is not there. And the higher the temp, the higher the pressure becomes..that is what High Termal Load refers to. So, if this high side presure gets too high b/c of high ambient temps, an added amout of air-flow across the condensor helps keep it in check. This air flow reduces the condensers temp and that directly reduces the high pressure..if the pressure get too high for even the aux fans to keep it in check, then you will see a compressor saftey cut-out sw ..These vary on different systems..
Your sw is pressure triggered, but some condenser fans are in fact temp sensed/triggered.
The refrigerant just has a higher pressure at higher temps, regardless if the a/c is on or not. Same as your tire pressure increases w/temp. It is a contained gas and a law of physics..
Just a SB mentions cars coming in that are running hot coolant temps b/c they are low on refrigerant [ low fan never coming on, but enough passive heat from condensor to effect the engines cooling ability], the same applies to the a/c fan where the complaint is the fan never comes on when a/c is on. You wind up with a hot running engine temp b/c you have a hot condenser in front of the cooling radiator, thereby restricting the radiators ability to tranfer coolant heat. .......BAD
Another reason for a no low fan can be [ and often is] simply b/c there is low ambient temps when the a/c system is on, so the condenser never needs assistance from the fan . [ never reaches high pressure cut-in]. This condition seldom cause high engine temps and is Normal.
That is why the correct diagnosis should be made with gauges to compare the sw specs to the actual high side readings...and evap temps.
Same problem as with a unit that is low on refrigerant, but different diagnosis b/c of ambient temp coming into the equation..that is why we referred you to eyesight..MOST common NO FAN on a/c system is low refrigerant, where you still have cooling, but not enough refrig to trip sw.
You were corrct in jumping the high side sw before anything else b/c you verified the circuits electrical integrity before getting into the refrigeration system itself. I see many guys just change the sw [ which means total evacuation. etc] when they really never needed one in the first place.
Clear as mud.........
In you newly aquired car, I would evacuate the system and recharge the syatem with the correct capacity charge ..that will probably do it...