The choice is yours.. as G3 said, if you want to give them a chance then now is the time. I think it is too early to pull the plug, but DO check to see if that queen is laying.. you said there was some brood in the first post if I remember correctly.. the queen will not lay more than the bees she has can cover. Adding a frame of capped brood will give her the bees she needs to lay. There is enough time for two full rounds of brood, and as stated, you can winter them as a nuc... FEED them, and use a robbing screen or entrance reducer to keep them from being robbed out.
Taking a frame of brood from another hive now still gives it time to rebound as well.
Having said all of that... I am also going to agree with Apis and Iddee. In my situation I would not hesitate to pull the plug. I do not have the time to tinker with them or fuss over them. I would consider it a learning experience. SEE if you can pull them through. I believe it is possible, I have done it in the past, as stated, provided the queen is capable. In a WORST CASE scenario, if October arrives and they have not built up enough to survive the winter in a nuc.... THEN you AXE the queen and combine them with whichever hive you have that is weakest. They will also have stored some of what you fed them, and you can use those frames in your other hives to boost their winter stores.
It is all a matter of what YOU wish to do, and depends entirely on your situation. I agree that the MOUSE or whatever the invader was could not have done that to a healthy hive and survived it. The scenarios are plentiful.. were they weak because they got into SEVEN dust in someones garden? Or are they weak because the queen is sub par?
