Will my lonely hen adopt babies?

[Chelsa'sChicks]

Lonely does not equal broody, so the likely outcome of a direct adoption attempt will be dead chicks.
What you could do is b roid the chicks in the coop with her (if your setup allows) so that by 4-5 weeks you can start integrating them. @azygous and @Blooie both have some great writeup on this.
This is my present setup that allows what I am suggesting:
View attachment 1269734
Those are 4 day old chicks in my brooding section with a mama heat pad for warmth and the adult hens they'll integrate with in a few weeks

This is 100% correct. They need to look and hear, but no touching. Hens that are not broody can peck chicks to death if they are not their chicks. Some breeds are calmer then others and may not do this .. I have a few hens that are moderately aggressive and fight my 7 month old rooster still who mind you is 8 or 10 inches taller then the hen. They will be curious and the longer they get to look at each other the smoother the transition when they meet face to face.

 

[mrshafer5]

Your hen does sound broody. When are you expecting to get the chicks?

I recommend proceeding with the plan to brood the chicks beside the hen. One way to tell if she is becoming receptive to brooding the chicks will be if you see her "tid-bitting" to the chicks. That is a sign of bonding, and you might then allow her access to them after they've been introduced for a period.

10 am. Tomorrow whats tid bitting?

 

[happyhens1972]

10 am. Tomorrow whats tid bitting?

Picking up small bits of food and dropping it in front of the chicks to try and show them what to feed on. It's what mother hens do to teach the chicks what they should and shouldn't eat x

 

[azygous]

What @happyhens1972 said, that action of offering food while rapidly uttering a high pitched chirping sound. This vocalization means a broody is calling her chicks to come eat what she's found.