Do IAPs Improve My Chances of Winning?

Not really. IAPs in the game are in the form of in-game resource called v-bucks and are distributed in quantities. With this, you can purchase the battle passes that includes a collection of items like skins, loading screens, and glider designs. Aside from the cosmetic features they provide, there isn't any buff-related feature from the any of the items. Even Epic stressed that they will not sell items that will ultimately give people competitive advantage, quoted:

“No. We will not sell items that give a competitive advantage. At some point in the future we will sell other things including cosmetics or compendium-like content.”

We hope that settles that! In addition to this though, there wouldn't be any way to earn v-bucks from playing through the mobile version of the game (as opposed to the grinding you can do in other platforms), as there is no PvE mode to do so. If you still want to earn them through daily log-in of the game and as you finish up on your "Save the World" missions, you can still do so by accessing/playing it in the console or PC version of the game. Nonetheless, your account’s progress will remain the same in all platforms.