No. The data in each direction is encrypted by TLS, using ephemeral keys.

Only the owner of the corresponding private key can initiate a connection from their public key, or receive a connection attempt to their public key.

Let's say you have alice and bob talking via a relay. Even if you have the private key of alice, you can impersonate alice to bob, but not vice versa. So you can't initiate a connection between the two.

To really intercept data you would need the private keys of both participants.