Yes! I do this too. Actually our vet suggested doing this for whenever we dropped my dog off for checkups/dental cleaning, so I started doing the same for my puppy and I’ve found him cuddled up to my socks or tshirt.
We also have an indoor ring camera to check up on him when we go out, @Silversitters we have always taken this down when we have sitters to respect their privacy, but also as Angela mentioned it’s against policy.