You should probably train with them up when learning, until you have mastered footwork, distance, timing, angles, and overall movement. For most professionals, this means never.
I mean, you can always try it, but against someone who even partly knows what they are doing it's going to be a bad time for you unless you are naturally the elite top 1-2%. Or basically, you just have to be miles ahead in skill in comparison to all your opponents.
That's what I think. I don't mean to discourage you from experimenting.
Here are some other difficult things that the very best pros can sometimes get away with:
-- Leading a combo or single punch attack with your rear hand first (instead of a jab)
(Mayweather Jr., Berhard Hopkins, Ali)
-- Putting your hands behind your back, sticking your neck/face out to taunt your opponent into attacking and then knocking them out when they try (Roy Jones)
-- Using the pull counter repeatedly
(Mayweather Jr.)
-- Dancing literally while supposed to be fighting (several)
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So the only reason why you shouldn't train/fight with your hands down is if it doesn't work for you, it's kind of a bad idea at first because there's no way it can work in the beginning stages, and at the higher stages it's still extremely risky to your health UNLESS you have already demonstrated that you can pull that kind of thing off.
The sign that you can likely get away with something like that is if you are having too easy a time with all of your sparring partners and competition, to where it almost feels silly. If you're that much better, everyone will be able to see it manifestly (including your coach) and you can start getting away with bending or even breaking certain rules just like Muhammed Ali or prime Roy Jones.
Good luck with that, hope you don't die