I agree, probably. You don't get guarantees but I'd try it that way.
Some people feel that a hen has to be broody a certain amount of time before she will accept a baby chick. Broodiness is hormonal and the hens need time for those hormones to run their course. That has not been my experience. I sometimes wait a week after a hen has been broody to start eggs under her. She does not leave the nest after 21 days but stays the entire time and accepts the chicks when they hatch. I had a broody fight another broody to take over after she had been broody for only about 3 days. Each hen is an individual.
Some hens will not accept baby chicks no matter how long they have been broody. Some kill their chicks when they hatch. They may be good incubators but not good mothers. That's rare but it happens. Some hens don't really kick over into full broody mode for several days when they start. Occasionally some even quit after a few days, the hormones didn't work right. Some hens imprint on their own chicks and won't have anything to do with any others. Other broody hens will try to mother any chicks they see. You never know for sure how a broody hen will react.
As I said, putting the egg under her is how I'd try it. The egg might hatch, it might not. That's something else you don't know. In my opinion, if it does hatch she'll probably raise it. She might not, I can't give you any guarantees.
If she does raise it, one potential problem time comes when she weans it. At some point she will leave it on its own to make its way with the flock. I've had that happen at three weeks (in the heat of summer), I've had them wait until well over two months (hot or not). Until she weans it she should protect it from the flock, mine always do but others have different results. This is if she raises it with the flock.
She will have spent that time teaching the rest of the flock to leave it alone. So the chick is integrated, which to me is a big advantage with the broody raising them with the flock. But chickens are social animals and like to be with other chickens. A lone chick may experience a rough time if it doesn't have another chick it's own age to hang with. The adults may not be that accepting of an immature brat hanging around. May, not absolutely for sure. Sometimes a lone chick has it rough hanging around the outskirts of the flock until it grows up. That's why we generally recommend a minimum of two chicks with three being better in case something happens to one. Sometimes doesn't mean every time. Sometimes this works out fine. A lot depends on the personality of the individual adults, each of them are different too. The more room you have the better your chances of it working out.
Some people in your situation would isolate the hen and chick for incubating, hatching and raising it. I don't do it that way but for their own reasons they like to do it that way. There are all kinds of different ways you can try this. Good luck whichever way you try.
