I really wish vets would provide medication in syringes. It's really soooo much easier to give the average cat a shot compared to giving them a pill.
They will, if you speak to them ahead of time and they're comfortable with it.
You can tell them that you already know how to give a cat an injection and talk them through how you would do it - if you don't already know, you can tell them so and they will train you. If the cat is hard to pill and will be stressed/dangerous coming in without sedation on board, it is in *everyone's* best interest to take the time to discuss it with the vet, get training if needed, and give sedation at home before going in - they don't want your cat to hurt itself or bite them.
I had a cat who was mean at home and an absolute psycho at the vet. She had diabetes and needed to go in often but she was a danger to herself, me, the vet, and the staff. We figured out a premed protocol that involved me giving her an injectable sedative at home, waiting 20 minutes, giving her an additional sedative orally once the shot had her calm enough that I could pill her, and then bringing her in fully stoned. It was not ideal but it was the best we could come up with. Remarkably, her day to day diabetes management was not a problem - although I could not pill her, she had no objection to twice daily insulin injections and the occasional blood glucose test.
My vets have had no concerns with me giving injections at home in many similar situations. It's made easier by the fact that I was a vet tech for 12 years so they are already confident in my skill set, but even if I had not been, there are plenty of owners who have to learn to give injections at home to manage conditions like diabetes, give subcutaneous fluids regularly, etc.
This is an old thread that seems to have been revived on accident, but I thought it was worth mentioning that this absolutely is an option and people should ask for it if needed, including asking to be trained on how to do it. I can teach a confident, non-squeamish owner how to give their cat a shot in under 10 minutes, and if it improves everyone's quality of life and safety, it's a win-win.