No. Snape killed Dumbledore for Dumbledore. Albus requested that he do it for multiple reasons. Firstly, to spare Draco Malfoy the damage it would do his soul to perform a cold blooded murder. Secondly, the Elder Wand would lose its potency if Albus died undefeated, and surrendering and agreeing to a death beforehand does not count as a defeat. (that one didn't work, since Draco's disarming of Albus did count as a defeat, and the Elder Wand became loyal to Draco). Thirdly, to spare him a long, painful and protracted death by means of the suffering inflicted by the curse in his right hand and arm.
There was also the fact that Dumbledore was already dying from a curse. He had little time left.