No he didn't. There's not a peep of Korah aspiring to Moses office in all of Numbers 16. The passage even repeats the offense so there is no doubt: Korah and his fellows accused Moses of taking too much on himself.
Your contention is simly not supported by the text.
Not Moses! Aaron! REEAAADDDDD!!!!!!!!!!!!!!!
“And Moses said to Korah, “Hear now, you sons of Levi: is it too small a thing for you that the God of Israel has separated you from the congregation of Israel, to bring you near to himself, to do service in the tabernacle of the LORD and to stand before the congregation to minister to them, and that he has brought you near him, and all your brothers the sons of Levi with you? And would you seek the priesthood also? Therefore it is against the LORD that you and all your company have gathered together. What is Aaron that you grumble against him?”