Would I be able to drop off an abandoned dog?

Yes.

Is it your dog? If it's a stray they have to hold it longer before it can get adopted or go into playgroups, it's sad. If it's owner surrender it's available immediately, he can get adopted or rescued, and he can be walked and go into playgroups. A lot of people say it's a stray just to save money but it's longer suffering for the dog.

Yeah as long as you don't tell them it's your dog you can....

Don't tell them it's your dog