No, PTC, it's not ok to punch a heavy bag with no gloves.
It's not ok to express anger in any way that harms you or harms others. There are plenty of ways to express anger (and all other emotions) without putting anyone in harm's way or causing any damage.
I know anger is an intense emotion, and people are often tempted to take it out on themselves. But that's just not right. Neither is taking it out on others. Most of the time, for you guys that suffer from eating disorders and related illnesses, taking it out on yourselves is the usual trend.
Either you're mad at yourselves for having anger and you think you need to punish yourselves for having that emotion. Or you're too afraid of what will happen if you express anger directly (several of you mentioned the fear that you'll be abandoned if you show anger) so you express it indirectly (which means: at yourselves).
But expressing anger by harming yourselves is a losing proposition all the way around. I know it seems like a good solution at the time. I mean, you get to be aggressive towards yourselves and that feels "right" and "appropriate" at the time- you think you "deserve" to be harmed and to have aggression aimed at you (you are absolutely wrong in that belief, by the way!). You also feel you are being safer and more in control by avoiding being "public" with your feelings.
Really, though, all expressing anger by taking it out on yourselves does is turn the anger inward where it festers and gets submerged and entrenched, building up over time (and, yep, making you feel you need to do more of that taking it out on yourself thing). So not only do you, in the moment, harm yourself through whatever method you're using to express your anger (at yourself), you aren't ever truly expressing the anger so it can dissipate and be done with. See? Really bad idea all around.
We all need to search for and develop ways to express anger that are healthy not harmful. So... are you glad you asked the question, PTC? (I'm sort of guessing you knew the answer already :)