I would try giving the food in small portions. Many cats gag and
throw up when they eat too fast or too much. The hairball problem is everpresent with them. So with a sick kitty it would be hard to separate out that effect.

For the short term human foods are okay, but they don't have taurine in them which cats have to have. If you choose baby food or tuna and feed for any length of time you'll need to add taurine to it. (ask the vet for doses). This is cheap and you can buy it in health food stores.

It is really tough choosing when to put a pet to sleep. We've done it 3 times and it never gets easier.

Try giving smaller portions of food. It may stay down better.
Mix in alot of water with it too.

My son has a cat with malformed kidneys. He adopted her as an adult. He has taken her to about 7 vets in his college town and all had different advice. He had an ultrasound to diagnose it.
She is living on one small malformed kidney(they think the other is not working)! He found that using regular food for her was better than the restricted kidney type. She is much happier on regular. If you read the link I gave it sort of echoes that.