Yeah without a band and audience, locked inside your bedroom.
Nobody in the world can tell which wood a guitar has at the stage, not the audience and not the player.
And no, tone would never affect my playing, I've been playing for 20 years and I always gave my best even when an amp was crap or stage sound was terrible, I always played the same way.When people pay you to play, there are no excuses, you have to play no matter how good or crap sound is, I remember one time I played around 2004 with a crap small roland amp with two 8' speakers, promoter told me there'd be good amps at that gig, well there weren't, I played the whole gig(about 1 hour) without hearing myself, yes without hearing myself cause I micked that crap amp but that stupid guy on the mixing board couldn't send it to my monitors and I couldn't stop the gig to teach him how to do it
There are so many different situations but the only one you can hear wood differences is sit alone in front of your amp and exchange 2 guitars with different woods but with the same pups.
But the difference IS there, regardless... and I'm sure you always play your best, but believe me, playing through a crap amp WILL effect the outcome of not only your tone, but the way you play as well. EVERYTHING in the environment while you're playing effects your performance, not better or worse, but overall.
You're right, totally blind I can't tell you if a guitar is basswood, mahogany or plastic (well, I HOPE I'd know the plastic one) but you can hear 'warm', 'bright' , 'dark', 'muddy', etc, and yes, even in 'live' situations. Be it in your bedroom or on a loud stage, and since 'tone' woods characteristics are normally, 'warm', 'bright', etc. based on the wood. You can often make an educated guess as to what wood you're hearing, so long as you're listing to a clean enough sound that allows the timbre of the natural wood to come through.
If you only play distorted, it's very hard to tell the difference... but even then, it does subtly effect your tone since you're final tone is simply a result of everything, starting with the guitar all the way to the speaker.