From a consumer standpoint, the answer is: "Maybe."

It really all boils down to the type of game, what the unlockables actually are, and how attractive these unlockables are to the player.

From what I've collected, unlockables normally do two things: Give the player extra in-game advantages, or make the player's items/equipment/appearance look much more attractive than what the game gives them.

If the game really is enjoyable and keeps gamers playing, then unlocking items that help them are obviously desirable to them. And if they play a multiplayer game which other players can show off achievements in the form of skins, avatars, or other cosmetic unlockables, then you not only want to look as cool as them, but also want to show off what you've achieved.

The issue with mobile games is that they aren't always played as long and seriously as actual console or PC games in most cases, so showing off your cosmetic achievements on your phone or tablet really don't account for much if other people don't sink a serious amount of time and effort into the game.

This leaves the in-game beneficial unlockables. If the boosts are presented earlier-on and the game rewards enough satisfaction to the player for his or her efforts while they're legitimately enjoying their gaming experience, then yes, they would theoretically be inclined to play more assuming the game doesn't become dull and monotonous.

But as I said earlier, it really is up to the developer how fun the game actually is and how attractive these unlockables are.

TLDR; Maybe. As long as the unlockables offered are done properly and the developer properly presents them either in a true cosmetic or in-game beneficial value.