Generally speaking, the answer to the question is "no".
Horses normally don't stuff themselves full of hay as long as they have ample pasture to go-roaming and be horses.
Horses on a dry lot, with nothing else to do, might stand there and eat until their hooves are pointing skyward.
Horses with insulin issues oftentimes have absolutely voracious appetites and will gorge themselves because they think they are hungry, thanks to the insulin spikes.
I have two metabolic horses. The 12 yr old has to have his hay weighed and put in a slow feeder hay net at night because he is one of those voracious eaters.
The 24 yr old is not. I weigh his hay, throw it loose in his hay tub and I will still find him munching on morsels in the morning.
I only have four horses and have never fed roundbales because they waste too much and I need to control how much all of them eat.
Thankfully, I still have plenty of pasture so I'm not throwing hay out but, when the time comes, I feed small squares and I measure what they get.
When their pasture grass goes down to really not tasting good, they will stay on the hay for about an hour, go out wandering for a couple hours, come back to the barn for water and munch more hay, go back out wandering, finally coming to the pasture by the house about an hour before dark to wait for supper. Sometimes they will munch the left over hay, sometimes not.
Even the IR guy who always thinks he's hungry does pretty good but again, he's got 22 acres of hills to keep him occupied
If roundbales are the only option, the painful alternative would be to cut it up with a chainsaw so controlled amounts could be given. And that only works if the horse isn't in a boarding situation