A puppy...I'd try to hold off for a while even after the vaccines. Remember, the vaccines are against diseases that can possibly kill your dog, but there are hundreds of other things our dogs can get that will cause you to rush to a vet or leave your dog under the weather for a few days.
Yes, this is true. My drop dead line in the sand would be that it's a no go until my dog was fully vaccinated, but you're right that I wouldn't want her to pick up something that made her sick, even if it wasn't life threatening.
Realistically, though, I would guess that a visit wouldn't be possible anyway until my dog was closer to the age of yours.