Short answer: yes. I've done it (boxing, not MT).
That being said, you won't be at your best. You might feel full strength, but if it's an intense fight, your strength will quickly diminish. You might even feel weaker at the end of the first round.
What's more, you shouldn't be doing any intense training in the couple days before your fight, so you won't even know just how bad it is until you are actually in the ring.
As has been said above, you will be a fraction of yourself. If that fraction is 95%, wonderful. If it's 70%, then it's not so wonderful. My personal opinion is that you shouldn't. The only fights of mine that I regret taking, win or lose, are the ones that I went into without being at or near my best. That's just me though. I wish I had set a limit of feeling 90% or better for all of my prior fights.