I just had a chick that couldn't figure out how to eat on her own for over a week, but she was otherwise normal. She would yell all night because she was so hungry (only did this two nights before I figured out she wasn't eating). She's alive and eating well now. You are NOT delaying the inevitable, depending on the situation. I've also had some similar to yours (lethargic, on heels) that were perfectly fine in under a week with a little TLC (it has been over a year since I last had one like that, so I don't remember what care I gave them).
For the chick I just had that wasn't eating, she ran around fine with the others, drank, and SEEMED to be eating (in reality she was just mimicking the others pecking at the food), but would hang out under the heat lamp a lot, and yell most of the night. Once I noticed she wasn't actually eating, I syringe fed her for a few days (wet down chick starter with vitamins & electrolytes AKA: Sav-A-Chick). I held her beak open, pushed a little bit out of the syringe (not inside her beak yet), then wiped off the tiny amount on the tip of the syringe into the front of her mouth, so that she could decide to eat it or spit it out. She would eat most of it. After a few days of that, I set her and a dish of wet chick food on the counter and poked at it with the tip of the syringe, lifting some of it out on the tip of the syringe. She then started eating it off the syringe by herself. Within a few minutes of doing that, she started eating out of the dish on her own. For a few days, she would ONLY eat the wet food, but after a while she started eating the dry stuff as well.
She's perfectly fine now. A little smaller than the others, but when they reach adult size, you won't be able to tell her from the others.
I still offer wet food morning and night to the chicks, because they go NUTS for it.
Another note: It REALLY helps if you spend time with them. It stimulates them, and makes them want to get up and move. Even just holding them and petting them helps. Otherwise they just sit under the heat lamp, depressed and feeling miserable.
Half the weight of the others at the time:
Weight gain after 11 days:
From a few days ago, next to her sisters: