Doubt happens. They are human. But I would be very surprised if it happened as often for them (in baseball situations at least) as we think and at a frequency we could relate to.
Even taking extreme examples, like facing Randy Johnson in his prime. Or Nolan Ryan. Or Hoss Radbourne, depending on your age and era of preference. We think players get intimidated, and they might be more so than if they were facing any of 1,000 other pitchers. But they still dig in. And they still have enough faith in their abilities to swing the bat. and none of them are swinging to get it over with and go sit back down, not even the lowliest utility infielder; they're swinging because they think they can hit this guy...