I think it would be quite rude to do so. With a dog there's always a small chance they might 'go' because of the other smells in there, but it's a guarantee with a goat that it's going to poop all over the floor.
Aren't you worried about the goat being near dogs? My dad's goats are deathly afraid. Even if yours isn't, do you trust other people to be able to control their dogs around your goat?
I've taken baby goats in Petco, and Atwoods (we don't have a PetSmart). When I have a bottle baby they generally go everywhere w/ me. Most the people at Atwoods know me (two different Atwoods), they know my dogs for sure, and recently I had one tell me to bring my Pot Bellied pig for a visit.
I took my newborn bottle baby to petsmart when I first got her. She was so tiny!! she weighed 2 lbs. The owner told us that she was a rare teacup pygmy goat
we knew she was just the runt of the litter. But we got her anyways and named her annabelle. It was so funny. EVERYONE was staring at us. All the workers there were wanting to hold her and take pictures with her! we went there and got her a little pink sweater and a pink jewled collar. adorable. sadly she died a few months ago.
RIP annabelle. I love you. I will never have another goat like you.