Is Shri Ganesh the incarnation of Lord Vishnu?
No. To my mind, Shri Ganesha might be a name priy (dear) to Shiva because of the connotation Gan (Bhooth Gan) Ka Ish (Lord of the Titans.) and therefore the name must have come with the Shaivism. The Earlier names have to be taken as Vigneshwara or Vinayaka. The Ganesha created by Parvati should be taken as the life of Ganesh Invoked into the the roopam (the form) she made as if life was breathed into it. This would clearly place the existence of Vinayaka as a entity primordial. The existence of Vigneshwara has to be pre-creation, pre=evolution, pre-differentiation. It must be side by side with Prakriti the Adi Parashakthi. The seed of the Brahmanda, which is consequent to name Lambodhara with AUM shape., The name VINAYAKA itself is very significant for the reason that VI NAYAKA. i.e. Lord of VI. What is V? V is Shunya, Ether, I is Air Vayu. VA is also Beeja Mantra of Mooladhara Chakra. Therefore, Vi-nayaka becomes the Lord of the first two Gross Elements Akasha(Ether) and Vayu (Air).