if someone's inspired and playing/singing great, it doesn't matter what mic is in front of them.
...or at least it doesn't matter much, relatively speaking!
as a sort-of answer to trock's question from my perspective:
There's a '90s made-in-Mexico strat at our studio. I think it does have a couple of the pickups upgraded. It's not knock-yer-socks-off but it IS "a strat" and basically does "what a strat does."
I have a 1958 stratocaster... a pretty damn good-sounding one... at home. I don't always have it handy at the studio. Sometimes when working on something, I think to myself "man, I didn't bring my strat, but this part really should be a strat" or even "I didn't expect to be recording guitar today, but this track could REALLY use a part..."
I have never once gone home to get my '58, nor waited until I had my '58 on me. Consequently, that MIM strat has ended up on MANY records.
Similarly, and slightly more literally-- I was sent an inexpensive but decent condenser mic for review once (I write for a magazine sometimes). It was so inexpensive they didn't even bother having me send it back... so here it sits, by my home computer, on a stand.
At least 10 times in the last year I've used backing vocal parts, or acoustic guitar parts, or percussion parts recorded on that microphone as part of final mixes. Once very recently I DID re-do a few "done at home on that mic" acoustic parts on a KM-86 the next time I was at the studio, because they were very exposed and had to sound very good. But there was also nothing particularly special about the performances being replaced, otherwise they would've likely been kept.
So I guess the answer is "it depends," for me.