If this has some effect, and it has as the price of Doge shows, this is going to be temporary. The market is bearish at the moment and Doge could not just rely on the words of Elon Musk for its rise. And this is not something new. So the effect will be of lesser degree than the first and probably second time Elon Musk showed support for Doge. And of course this is not Tesla cars that could be bought using Doge. This is just Tesla merch.
If the doge not relying on elon words anymore on what it could rely ? doge has no usecase and future plans, this coins price will increase only if people are on hype for this coin. So i think it's better to leave this coin for a long time investment since having profits from this coin is really speculative.
Investing on any coin that hype when someone blow it up is a high risk investment, could grant much profits if the investment been done in the right time but could make loss if wrong.
Actually, to be fair to Doge, it has gained a certain level of popularity even before Elon Musk came into the picture. Even if Doge was created as a meme coin right from the start, it has actually reached the top 10. This was way before Elon Musk took a role in its market. Before Elon was shilling for Doge, and even if Doge is stagnant in its development, it has a use case or two which made it thrive for a longer time. Doge was great for tipping, for gambling purposes, etc. It never died after many years of crypto market competition.