The way today's alternators work is very different from yesterday's units. Today's alternators are very high output devices in a very compact package. This design has some "trade offs". Today's alternator's are no longer self exciting. The battery is used as an energy store to "buffer" the step load changes as will as to provide the excitation voltage needed to "kick start" the field winding into work.
In practice for today's cars no battery = no alternator.
But wait. If this is true why doesn't the motor die if the battery is disconnected? The answer lies in how alternators and excitation work. In practice when the motor is running in a steady state it is possible to disconnect the battery and the alternator will continue to put out. The problem comes when there's a large step load power change. Without the battery to act as a damper the voltage could dip as the regulator is attempting to adjust.
IF during this delay the voltage dips too low, the alternator field coil will loose strength (excitation) and shut off. Without a ready battery to provide excitation the voltage regulator can not restart the process.
Virtually every system in today's car relies on a stable power source. But consider the high energy ignition system that is supplying spark. It's it hard to see how the ignition system would be affected by low system supply voltage? Would a drop in RPM's be expected
IF the spark were weak?
I'm a big believer in starting with the basics. EVERY trouble shooting session should begin with a review of the battery and charging system. Does that mean replace everything. No. It means check and test that it's performing at some minimum level. At the very least perform a visual inspection.
The good professional mechanics know this to be true.
If still uncertain that there even is an alternator problem why guess? Test! If there's is an problem with the charging system it will show up on a tester. For a major voltage problem that bad enough to starve the ignition this has to be an event that is measurable with a Volt-Ohm meter.
IMO If this were my car and testing showed there was a problem with the alternator, I would not take the chance of going on a wild goose chase. I would always stop and fix the alternator/charging system before performing any additional trouble shooting. This goes double if spending $$'s on parts is involved.
Bonus thought for the day. Can you "bump start" a modern car with a TOTALLY dead battery?
Howto perform charging system voltage drop test
https://www.stangnet.com/mustang-fo...perform-charging-system-voltage-drop-test.56/