Predicting HFSS Wave Port Modes
Yes, this is generally correct.
The frequencies of the cutoffs for standard TE and TM modes can be found in nearly any textbook. Hybrid modes... not so much. Most likely, you'll have to calculate these yourself, or perhaps more efficiently, just observe them in simulation.
HFSS can be quite useful when dealing with higher order modes in waveguides but matching the fields observed and the textbook modes can be a bit of an entertaining exercise. In circular guide you have the added fun modes rotating in the waveguide and controlling their particular directions. Watch the alignment carefully as coupling reported can be misleading particular if the alignment is not controlled carefully. I generally ask for a few extra higher order modes to make sure nothing gets missed in the simulation. Lots of pretty pictures to try to sort out.
By the way for even more fun the simulations can get really big with higher order modes excited.
Simon and Waddel are useful references as well as he usual waveguide handbooks.