I remember years back being on a regional turboprop (whomever the sub-unit of Delta was in the 90's) from Salt Lake, to Twin Falls, ID, where the one engine just plain didn't work.
they may have gotten it running just long enough for take off, but it was long enough ago, i don't clearly remember.(I was probably 10-12yrs old)
flight was smooth sailing to those of us in the passenger cabin, if you didn't look out the right side windows, you'd never have known only one engine was running...
however if you DID look out those windows, it was a bit jarring for a second to be up in the air, and see the prop stationary...