Yes, she is definitely wanting to brood.
Before placing eggs, I wait at least 2 to 3 days of really solid brooding, meaning they stick to the nest only getting off once a day to go right back to the nest. Hens can have a pre-brood stage where they are on for a number of hours but then get off for several hours. They'll do this while they build their clutch.
I have main coop brooded and have a designated brooding hutch. For those hatches I really desire (purchased breeder eggs or a particular line I'm wanting), I always use my hens in the brooding hutch because they have isolated nests and their own private grow out run (which has a fenced run that the flock grazes by to help with integration).
Coop brooding comes with its own set of issues. If you have a dominant hen, she will generally hold her own and not be forced off the nests. However, the foot traffic often crushes eggs. It definitely can crush hatching chicks (lost a number that way). In my experience it is far better to put up a protective screen barrier so that the hen cannot be encroached upon especially during the lock down phase (last 2 days).
Each flock is different, and how you brood depends upon your flock dynamics. In laid back flocks, especially those with a good rooster keeping peace, coop hatching within the main flock can be highly successful and a joy to watch (with the caveat to isolate during lock down).
However, if the brooding hen is less dominant, others more aggressive, or foot traffic especially heavy in the "golden" box, then the best course of action is to isolate the brooding hen to give her the space and safety to hatch chicks.
Good luck with her and a crop of chicks. Let us know when you set
LofMc