It’s not a bad idea, but it’s not that black and white. I work on a game called Notoriety, and we only sponsor the game for when we push out brand new content. When we pushed out an update that allows players to get skin patterns for their weapons, we peaked up to 3,000 concurrent players, and finally pushed our game rating from 89% to 90%. Reaching out this update was a combined effort of changing the title and icon, using sponsorships, and using game update notifications.
If your overall goal is to attract more players, then define the audience you already have, figure out what they want from you. At least once a week I hop into the game and chat with players and ask them a series of questions towards the game. Work towards meeting those needs or coming up with an idea that they might like, update the game, and the sponsors & notifications will complement it.
tl;dr - update the game first, then follow through with sponsorships & other tools, regardless of the time and day