You have no choice but to include the arrest on the I-751, because it asks about arrests and to do otherwise would be fraud. I can't tell you what the outcome will be. You should talk to a lawyer about your course of action, including whether or not, since it is overdue, to wait until the charges are dropped if he is confident that this will be the case (although you can never be sure).
My understanding is that the basis of the I-751 is simply to ensure that PR status is still valid, particularly to verify the legitimacy of recent marriages. Filing I-751 will put them on notice of the arrest. I don't think it can be denied based on an arrest, but if it is a deportable offense (I can't say based on the details you gave, but it may well be, forcible touching under NY law is a crime of moral turpitude), then they will definitely want to know the disposition. If the charges are dropped, then I would guess that he should be okay. But again, since he needs a lawyer for his criminal case anyway, this is something to ask a lawyer, especially one familiar with immigration and criminal law. You want to be sure that the charges are actually dropped and he is not entering any plea or agreement that USCIS would consider a conviction.
As for the late filing issue, I have no idea. I think it is possible that he could lose his status and be removed on that basis and have to start over, I don't know, and I don't know if that together with the arrest makes his situation any worse, but I think in general he is out of status and removable now and it is at the USCIS officer's discretion as to whether there was a good cause for late filing. See
http://immigration.lawyers.com/ask-a-lawyer/Late-Filing-Of-Form-I-751-6583.html for instance. If he was on active duty in the Army that would be a sympathetic reason if he filed immediately after discharge, even though it is not an excuse by itself.
Just a wild guess but it may be best to file it immediately and send in information about the disposition as soon as charges are dropped, assuming that happens. If not, they will probably either deny the application or ask for information about the outcome before ruling, which means that a conviction would likely lead straight to deportation.
In other words, lawyer lawyer lawyer. If he had filed the form on time and hadn't had this misunderstanding he'd be fine without one, but as it stands he is in serious danger of permanent removal.