Goodman furnace ignites but fan won't run
I have a similar Goodman furnace and have done troubleshooting on it for similar problems.

Your thought is correct - if the burner fires but the blower does not start, that will cause the burner / heat exchange to overheat. When the high limit trips, that is normal and the switch is doing it's job.

Some possible causes and troubleshooting for the blower non-start:

Bad capacitor (the PSC blower motor needs the capacitor to start/run). Disconnect the cap and test with a multimeter on Ohms setting.

Blower stuck  The blower squirrel cage should turn freely if you push it by hand.

Bad motor  Test with a multimeter on Ohms, there should be low resistance on each winding. Infinite resistance (open) on a winding is bad. You might try selecting a different speed.

Bad control board  Test with a multimeter to see if the board is supplying power to the motor. Note there will be different terminals powered depending on the selected speed.