Will Ambire Wallet be supported directly by new DeFi projects, even if it didn't cooperate with them yet?

Yes.

Ambire Wallet does not require anyone to cooperate with Ambire, in order to be supported, as Ethereum and all other EVM chains provide out-of-the-box composability. This means that for a DeFi app, it doesn't matter if it's called by an EOA (externally owned account, or a normal wallet), or any smart contract.

Just an as example, dApps like DeFi Saver and Instadapp can perform actions on your behalf using the same composability principle.