I can't tell lefthanded from righthanded musicians by ear, but it seems like a person should be able to - that it makes a difference, in some fairly deep ways. There are classical musicians who can tell when a player is using a different bow, after all.
With the exception of Ringo Starr, of course--a left-hander who set up his kit in right-handed fashion. Apparently, although who knows the veracity of this claim, this was why Ringo couldn't play proper rolls. Personally, I think he simply had no desire to--and his drumming really doesn't suffer from it.
Conversely, Phil Collins--who was very strongly influenced by Ringo--did set his kit up in a left-handed fashion. If you listen to "A Day in the Life" alongside Genesis's "Cinema Show," the influence is very much apparent--though the latter is far more... involved. And actually, Collins does sound very much like a left-handed drummer to me, though I can't quite place why that is.
With piano, organ, harmonium, etc., the difference, however imperceptible, is still there... I think. Nico, on the suggestion of Ornette Coleman in consideration of her very low voice, tended to play the melodic bits with her left hand and the harmony and rhythmic underpinning with her right. Largely homophonic and very much evocative of both ancient musics (the Greeks), pre-Baroque, and Carl Orff.
And honestly, I think that I sound left-handed. I've never developed sufficient skills to play the pedalboard well, just very basic minimal stuff, so I often tend to use my left hand as though
I were playing a pedalboard, and I've installed a switchable 12-18 note bass pedal circuitry into my harmonium to compensate. Kinda weird, yeah, but a lot of combo organs were also set up with such options. And really, whether I "sound" left-handed or am simply asserting the primacy of harmony, rhythm, and tone coloration over melody (I'm a big fan of Messiaen and a lot of the contemporary Polish composers) is very much debatable.