Yes Alfie does this, in fact he does it anytime he is excited. He also insists on taking a toy outside with him for a wee, I usually try and grab it before he goes outside because he always leaves it outside in the rain
He always has a toy in his mouth when we go out for a walk, I then have to grapple with him to let go and leave it in the hall, just recently he has taken to grabbing the draught excluder. He holds it in the middle and it is about 3 ft long, looks hilarious, like he has a massive sausage in his mouth.