I don’t think it’s so much a matter of “if” a mariner can develop a “feel” for a ship but rather a matter of how quickly and how well.
Comparing direct observations against instrument measurements and the result of calculations is going to be the quickest most efficient way to gain proficiency. All methods have errors.
A deep-sea chief mate has the experience and access to all the information required. The characteristics of a tender ship vs a stiff ship is described in books on stability. In La Dage & Gemert it’s in chapter one, page one.
The stability booklet has a section where the rolling period vs GM is given in tabular form. As @Hogsnort mentioned this can be checked by timing the rolls. The NWS observation form requires sea height and wave/swell period.
Once the basics are understood by using the instruments (watch, inclinometer, anemometer (for wind heel), draft marks / gauges) and calculations; then by being observant other methods of estimating will be discovered and developed.
In time intuitions will become improved.
I’ve posted about this a few times, for example here. Seamanship, Navigation, Piloting, Metis Techne
And it’s possible to go too far the other way:
The Seaman’s Eye Fallacy