It looks like the answer’s no -
It’s hard to see how Monzo would fund the interest payments because aside from the overdrafts (which will initially be Monzo’s only meaningful source of revenue), it sounds like they’re not planning to do anything with our deposits that would earn significant money.
But obviously if you want to earn money on your balance, then you will be able to invest it, through a provider like MoneyBox who will hopefully be integrated with Monzo via Monzo’s marketplace.