Yes, the snake admired its beauty. The snake that coiled itself on the doctor's arm, kept staring at its reflection in the mirror for a long time, enjoying its beauty and appreciating its form. The lines supporting this are:
'But it was certain that the snake was looking into the mirror. Was it admiring its own beauty? Was it trying to make an important decision about growing a moustache or using eye shadow and mascara or wearing a vermilion spot on its forehead?'
'From there it crept onto the table and moved towards the mirror. Perhaps it wanted to enjoy its reflection at closer quarters.'