Assuming it’s the correct size and the straps are properly adjusted; no. If your dog is trying to escape the harness, though, you should consider introducing them to it more gradually, and double checking that the fit is good.
Regularly checking for this proper fit is vital for keeping your dog safe, as well as preventing them from sneaking off. Dr. Susan Nelson, a veterinary professor at Kansas State University, advises that when dogs pull on the leash wearing a poorly fitting harness, there’s a potential for chest injury.
You should also remember that harnesses can be too tight as well as too loose. You can tell a vest is too tight if it chafes, causes rolls of skin to gather about the dog’s neck, or leaves indentations when it’s removed.