I think it depends on the context. To be picky, you could just send out a lot of resumes, and I as a prospective employer wouldn't have any clue how many you've sent, as long as you are still at your old company the whole time.
However if you have a good emergency fund, your old company folds, and you are being picky, people start to suspect you are unemployable after a bit.
I also am kind of picky although I am not sure how wise that is in the current crisis.