If a patient came to see me in an emergency appointment, and had no medical need to see a doctor but had come in solely for a sick note, then I'd feel disappointed that an appointment had been used for an administrative task when it could have been used to give another, unwell, patient medical attention.
I don't think you should use an emergency appointment for this - ring the surgery and request a phone call with a GP instead.
If you're still ill and actually need to see a GP, then I think it would be reasonable to go in, and ask for a note while there.