Yes it will, but not directly.

There are different measures of the money supply:

Monetary base: amount of money printed by the central bank, plus bills and coins. The U.S. monetary base is currently  $5.2 trillion
M1: All the money in all the bank accounts. This is what people consider to be their money. The U.S. M1 is currently $7.1 trillion
M2, M3, ...: time deposits, loans, ETFs, derivatives, etc.

Now, here is what bitcoiners who believe in the only-21-million-bitcoins myth overlook: While the Bitcoin monetary base is (or will be) 21 million, the Bitcoin M1 will be much higher when banks, exchanges, and lenders lend out the bitcoins that they hold.