If Scotty, Geordi, O'Brien, Torres, and Trip were each tasked with providing medical care who would perform the best?
Assume a mass casualty type situation. Something along the lines of AR-558 with physical wounds ranging from phaser and disruptor hits, to concussions, broken bones, and the like.
Each Chief would be from roughly halfway through the run of their series with whatever knowledge and experience they had at that point. Each would have access to whatever kind of portable medical kit a medical officer of their time would have brought for such a situation. There are no able bodied personnel to help. No they don't have access to a transporter.
Geordi, his visor can pick up on all sorts of things. He's operated on Data so often, and has often shown the capacity to apply theories across disciplines.
Scanning bone breaks and seeing them as engineering puzzles, repairing ruptures, understanding stresses, seeing heart beats and heat signatures....
...100% Geordi hands down. Plus he's good with people.
Of course in terms of real life, James Doohan (Scotty), as he's a WW2 veteran.
I think we can pretty safely put Scotty and Trip at the bottom of the pile. They've never shown any specific aptitude for medical work and I think 24th century Starfleet basic medical training and technology helps everyone else. Of the remaining three, Geordi seems like he would be very nice and try to be as helpful as possible about your injuries, but I'm ranking him 3rd overall. I don't recall O'Brien ever doing anything on screen to indicate his medical competence, but we can guess that maybe he's seen enough combat to have picked up some of the basics, so second place to Miles. Torres, with her extensive knowledge of programming and reprogramming the Doctor (enough to suggest a DNA re-sequencing of her own baby to the Doctor [Lineage, Voy]) and the fact that her year at the academy may have been a double major in engineering and medical [Extreme Risk, Voy] makes me put her in first place.
Hmm, interesting logic; my first reaction is that even if I program a robot to hit a golf ball I still wouldn't be any good on the links, but perhaps there's enough medical theory that she'd have to encode that she would be the top doc. I would have expected the original program to already have the knowledge and skills useful in OP's scenario, however.
I think all the engineers would have transferable skills, seeing as surgery is basically engineering/plumbing on living things.
Torres was also part of the Maquis, a severely understaffed organization, so it's fairly likely she had to pull double duty as a medic at some point. If so, she has prior experience. O'Brien is the only other one likely to have that since he was a foot soldier for a bit.
Yeah, now that people mention it I do think the VISOR would help quite a bit. Early on in TNG he even says he can detect if humans are lying from the minute physical changes (although the writers clearly drop that later, see his record at poker). Clearly that should be able to pick up all sorts of problems like internal temperature fluctuations and heart rate and in fact it does [The Enemy, TNG]. But what we don't see is Geordi ever fixing those things on a humanoid on screen. So he might be better than O'Brien, but I still think B'Elanna has the edge overall. Even if my logic is iffy (and it is: she fixes the Doctor so she knows about doctoring? Eh) on screen other characters acknowledge her medical skills. Including the Doctor, who gives her genetic re-sequencing idea serious consideration before she reprograms him. Would she be a better medic than even Tom Paris, who has a lot of practice but clearly doesn't like the work? I doubt it, but I'd probably take her in a life or death situation over the other engineers based solely on the primary sources.
Reno did pretty well for an engineer when she kept the Hiawatha crew alive. She didn't really treat any of them, but she approached the situation from an engineering standpoint since the body is basically a machine, and she kept the machine running.
Of the ones listed, Scotty and O'Brien would be the most likely to just store the injured in the pattern buffer for later, proper medical treatment (like Dr. M'Benga did in SNW), so I would say they would perform the best.
Edit: Didn't see your transporter bit. I still think Scotty and/or O'Brien would improvise something along those lines and solve the problem with the pattern buffer.
I'm specifically disallowing the transporter trick because the scenario is about making them provide treatment. Same thing as making sure they don't have any able bodied help to divest responsibility to.
Consider this a tuned holodeck training designed to diversify their skillset.
Since we already know, thanks to Pulaski's ageing incident, and the Picard, Ro, Guinan Kid incident, that cures are as easy as stamping a previous pattern onto them during transport, technically any one of them would be better than an actual doctor.
Throw them into the pattern buffer, upload the last stored healthy pattern from their most recent beam-out. voila...all fixed.
I've seen some great answers to the question as asked. I want to also toss the new-Trek engineers in there: Stamets, Billups, Jankom, and Pelia.
Jankom would be awful. Terrible bedside manner and a predilection for percussive maintenance do not make for good medical outcomes.
Billups would likely not do well either. Granted, we don't know much about him, but it seems like he's a competent but not outstanding chief engineer (let's face it, that's kinda the point of the show).
Stamets would freak. He would repeatedly note that it's actually his husband who's the doctor. But he'd probably end up doing a decent job.
Pelia has the distinct advantage of centuries of experience in her favor. It's entirely possible that she was a doctor at one point.
And, honorable mentions:
Hemmer would probably shock everyone by being amazing at the job. He would probably show some unexpected advantages to being blind as a doctor.
Jett Reno actually did this scenario, in her first episode.