Yes, I would think it would be, also it would if it were to get in its eyes, it would be horribly painful. If you don't want to get a puppy shampoo then perhaps use a mild baby shampoo at a weak solution. Then rinse and rinse and rinse again!!!
Personally, I would think a puppy shampoo is not that expensive, they have a some good ones at Wal-mart and Target and look at the Petsmart and Petco too. They have the kind that won't hurt their eyes as much just as they do for children's shampoo.
I believe Dawn is what they used to get oil off of the shore and water birds when the oil tankers leaked oil into the oceans and beaches. Good advertisement to show how well they cut grease! So if your puppy gets into an oil slick, Dawn may be the way to go, but invest in a gentle puppy shampoo, you'll both be happier
Oh, and always rinse really, really well
