Nope. Coinjoin works by having a transaction with inputs from various addresses and outputs to various addresses. The size of a transaction depends largely on the number of inputs and/or outputs. While batching transaction would make the size smaller, it would only be applicable if the transaction has one or only a few inputs.

For Coinjoin, each input would correspond to at least one or more output. As a result, the size used by each participant could be about the same or even bigger when compared to the scenario where they are making their individual transactions.

It's highly impossible for the protocol to recognise which transactions are meant to mix coins; any flags would potentially weaken the purpose. Bitcoin would likely prioritise scaling over anonymity.