It might cut off peripheral vision a little, but it’s certainly not the worst idea I’ve read today. Given the option, I’d rather use one as an improvised weapon, but it should protect against blows to the head and face. I mean, it is designed to protect against head injuries, so it should be better than nothing.
If the attacker is swinging a baseball bat or hammer, I’d worry about neck injuries if the weapon connected. But, against an unarmed attacker, the biggest risk would I can see be someone grabbing the helmet. If it’s properly secured, this shouldn’t be worse than someone getting a firm grip on your head. The helmet would protect against gouging, and should provide some protection against being bashed into walls.
The one big downside is that armor traps heat. It doesn’t really matter what kind of armor we’re talking about, this is one of those universal rules. For enclosed helmets, that also means breathing is going to be harder. This is part of why you’ll see articulated visors on plate armor. It’s there to allow the combatant to catch their breath, and vent some of the heat whenever they have the opportunity to.
Your character will heat up quickly and won’t be able to vent it. They’ll get winded much faster than they would if they pulled the visor up. Though, at that point they’d be sacrificing protection. The solution is to end the fight quickly, but, they’ll want the helmet off as soon as the fight is over.
One thing, I’m not certain of: it’s possible, between the increased perspiration and heat you could end up with condensation on the visor obscuring the character’s vision. This is kind of an issue with motorcycle helmets in general. Some models do have vents designed to deal with condensation and fogging under normal road conditions, but I don’t know how well they’d be able to keep up with the additional heat and moisture from combat.
You’d probably also need to replace the helmet if it took any serious hits in the fight. But, I’m inclined to think it would be better than nothing.