if you want to breed more chickens (we are all bad at chicken maths) then sure, put some fertile eggs under them on the same day (that way you will have hatches on the same day which makes things easier), but do it ASAP as being broody for 4 weeks already will have already have taken its toll on the one thats been broody for 4 weeks. Do be aware however that at least half of the chicks will be roosters, so you need to have a plan for that.
Giving them eggs is unlikely to affect their broody behaviour in the future.
They will do all the work, so just leave them to it and don't force them off the nest - they will know when the time is right to go and eat / poop.
You will need to do some planning for when the chicks are born however. What you do will depend on a number of factors, including:
The size of your coop
The number and ages of your flock
Whether you have a run or they free range
I have a mini-coop that i use for mum and chicks which is portable. The rest of the flock can see them, but can't touch them and i can put the mini-coop outside for them to do chicken things during the day. After a few days i move them to a large portable coop which has a run attached, but i do let them mingle with the main flock under supervision for short periods of time. By the time they are 3 weeks, they free range with the rest of the flock, but they still have the mini-coop inside the main coop (a shed) in which to sleep. Mother hen decides when its time to move them all to the main roost with the flock.
If you do not intend to raise more chicks, you can break broodiness by putting the broody hens in a small coop / kennel, suspended above the ground for a few days (with food and water). The cooler air circulating around them and being generally cheesed off at being separate from the flock members seems to snap them out of it.
Hope this helps a little