I would heartily recommend such training. Your level of training is at least as important as the gear you are carrying; no, more important. I would prefer to be handled by a knowledgeable person with no gear, than an untrained, or minimally trained person, with all the goodies in the world. I have personally seem what a good MD can do, thrust unexpectedly into an emergency, with absolutely minimal equipment.

Patient survey and assessment, including the detection of some fairly subtle conditions, is absolutely essential to providing good care.

Note that your TCCC has space for entries concerning BP, respirations, and other vitals. The folks you hand off to will be glad to get that info.
Now, frankly, I am a very rusty EMT, and protocols have changed to some extent, since I was active (70s and 80s), so I would welcome the comments of more current, informed persons.