Tough question to answer. Let me share some personal experiences.
Back when I was training seriously we had a standard training technique where the senior members had to walk from one end of the training hall to the other (about 20 metres) while 4 other people tried to stop him. Each 2 metres or so another, more senior member, would join the group trying to stop you. No strikes were allowed by anyone involved, only grapples, and a take down was considered to end your trial. I’m not a big man by any stretch (182cm, 75kg), and I would never have described myself as more than competent at my peak.
But I could easily move with up to 4 people hanging off me. These were of course the least skilled fighters in the class, but they were all fit young people. On my best days I could make it 15 metres or so and have 10 people trying to stop me. I never made it the length of the hall but it was only the well trained fighters who could stop me. The senior members could get the whole 20 metres about 1 in 3.
It’s just not that easy to take someone down without using strikes. While we didn’t specialise in grappling we did cover the basics including all the classic JuJitsu/Judo takedowns so all the senior members were proficient. Even using jujitsu/judo style techniques it’s incredibly hard when the person you are attacking knows what to do you prevent it. In fact having more people around often made it easier because they got in each other’s way and could be used to prop you up and prevent throws from working.
While this was a training exercise and not necessarily applicable to reality, I’m going to say that I wouldn’t place bets on untrained people taking the bloke down at all. The idea that they can just wrap up his legs and push him over really doesn’t ring true to me. I know that untrained people don’t think like that, they inevitably grab one leg. And I doubt if any untrained person could push me over in that situation without being disabled by me. And I say that while acknowledging that I am not and never have been a particularly good fighter. Against untrained people even a little training gives a huge advantage.
Next example: I was out on the town in my younger days with a mate who is a TKD instructor. He’s solidly built, but not the supersoldier described in the OP. With my own eyes I saw him take out 7 men single handed. (And before you ask, he requested that I stay out of it). The fight started inside a pub and he used the environment to his advantage: placed himself between two rows of poker machines so only two people at most could get at him at a time and used one disabled person as a shield. He took out all seven in less than a minute I would guess, and I see no reason why he couldn’t have taken out 20 or more.
He was a lot better than me (obviously) but still not Chuck Norris on speed. Once again, this is the difference that training can make. A trained fighter uses environment to advantage. If the brokers start attacking this guy en masse he’s going to use the terrain to advantage so only one or two can get at him.
Like Fotheringay-Phipps says, unless he gets crushed by sheer weight of bodies he’s going to keep disabling people until he runs out of breath. And if he’s as well trained as described he’s going to use the environment to ensure he can’t be crushed by a weight of bodies.
As the OP is posed I’m going to say the bloke will rampage until he runs out of breath. That’s probably going to be 40 or more people and will take a matter of minutes if they line up waiting. If he has to search them out within the building then he’s never going to exhaust himself and will keep going indefinitely.