I've called for an appointment but have not had to wait long when I got there.
First time is not usually a problem. Whenever we've had an animal that was obviously very ill, they've been very good about getting them in sooner than later. If your pet is in a very desperate state (unresponsive, drooling, etc), then just bring them straight over... they will make it work if your pet needs immediate help.
I've always called for appointment for my sick animal, typically they are prompt...sorry, not really answering your question. I've been happy with this vet.
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