I had an experience singing in a 60+ voice chorus that sometimes was so loud I could only hear my own voice by blocking one ear; even with cupping I was barely audible to myself. Obviously, neither cupping nor plugging one's ear is an ideal visual message in performance. Normally I sing quite in tune. Yet as others have said upthread, not hearing oneself can almost guarantee singing out of tune. I found that to be the most true when trying too hard to hear myself, either from oversinging (usually going sharp) or insecurity (usually going flat, "hiding under the note").

In that acoustic situation, sometimes I've found that I have the right note when I CAN'T hear myself, a very uncomfortable thing to do I should add. I learned this by using a hand-held voice recorder, which held to my chin picks up my voice in front of the other sounds, and then trying different approaches. It's very un-nerving, trying to sing according to the feel instead of the sound--but sometimes the less I feel, the more perfectly I've matched what's around me. When I can hear my own sound most clearly, it's because it is different from the notes around me, or it's out of tune with other parts I can hear. In western music, the scale and pleasant harmonies are based on natural overtones so when you have them right, the soundwaves are quite literally in synch.

That same trick was helpful to some others who had trouble tuning even in quieter passages, when they'd usually be under the note. Using this approach, when they didn't hear their voice as much or even at all (but could still feel it in their throats so yes, they were still singing), they were tuned much more accurately.

Of course at some point, singing by feel won't strictly apply, like if the volume is so high that one cannot even hear a wrong note. Also when the desired interval is less than a major 3rd, the correct notes can and should create some buzzing sensation which (more buzzing the smaller the interval). Getting to know these supplementary "sounds" can help to place a note correctly in challenging acoustics. all in all, when dealing with an intense acoustic setting, it's worth experimenting with in rehearsal.