For those who understand Bitcoin better than me: does it increase the anonymity of my coins if I swap wallets with someone?

For example, let's say I have a wallet.dat "containing" 50 BTC and so does a trusted member of this forum.  If we exchange wallet files, does that improve the anonymity of my coins?

Of course, once we receive each other's wallets, it would be wise to send the coins into a fresh wallet, preferably one created on an air-gapped PC or in a LiveCD.