YES! It's called overtraining and it can be worse than not training at all.
I heard that going all out to fatigue is good once in a great while so that your body isn't shocked in an all-out situation (i.e. competition) provided that you're very careful with it and take all steps to avoid injury.
Well see there is a difference between training super intense (ex; hitting the pads till you almost barf) and training past your recovery limits (ex; training soo much that you don't recover fully for your workouts. When it comes to training intense from what I've heard you should not train like youre dying everytime, same with lifting you shouldn't max out every day or your nervous system/strength will go stale. All progress should be gradual, fighters train different 2 months before the fight than they do 2 weeks before the fight. Lets say you're a professional fighter, you'd want to peak before the fight and not a month before or your condition will go down by the time the fight is due. I remember Bas saying you should train cardio about 80% of your capacity (intense wise) most of the week and go all out maybe once a week if I remember correctly. Just puttin in my two cents, hope this helps.
I guess the best advice is listen to your body, like yomon says "everyones different". Pay attention to signs like irritability, insomnia, fatigue, acne, nervousness etc. these are all signs of over training. When you overtrain you're most likely taking steps backwards than forward. It's good to have heart but your head should always come first when it comes to this.