I don't think there is a problem with it, but it wouldn't be something I'd do. There are tests where they need to stay for a few hours or whatever and that's fine, but this would be an annual visit. No appt. means no meeting with the vet and I would not like that at all. Everything would likely go through the tech and you wouldn't be talking to the doctor. Totally up to you. I know for me, I always have something(s) to talk to the vet about and would get really irritated sending my questions through a tech. So I think it's an individual thing.
Also, if it's a new place and you've never met the vet, it's probably best to do the first visit while you are there. Wouldn't want to leave your baby there when you don't even know if you are comfortable with them or not...
BTW, rabies and DHPP are best given on different days.