My parents leave the dog tied for up to 1/2 hour. But that is in the back yard, and even then some roaming dogs did get to him once, and some lady was feeding him treats one day.
Usually they set the timer for ten minutes, but he gets 1/2 hour in the morning.
I think a puppy is much more vulnerable than an adult dog. They can be stolen easier, bullying or teasing will have more lasting effects, and getting attacked by whatever can really be bad.
Anyhow, it is an ok question, but my guess is that you are going to get a lot more no's then yes's, and you should qualify 5-10 minutes.
Also for a pup, you want to be there so you can praise any pottying.
Heidi Ho, Odie
Joy-Joy, Bear Cub, Hepsi-Pepsi
Cujo2, Karma Chameleon
Ramona the Pest, Kojak -- who loves you baby?
Tiny Tinnie, Susie's Uzzi, Kaiah -- The Baby Monster.