Can I connect a FTDI adapter without disconnecting a Bluetooth board ?

Hello,

For a wireless project I have a Bluetooth board (Sparkfun BlueSmirf Silver) connected to a Pro Mini board. If I create the right connections, may I leave the Bluetooth adapter connected to the Pro Mini when I connect the FTDI USB to serial adapter to load the code ?

Thank you for helping.

Depends what you mean by "right connections".
Both parts want to connect to the Serial lines, yes?
So you are proposing some switching/muxing scheme to select between the two?
The Promini Tx can go to both, that is not a problem.
Preventing both device's Tx lines from interfering on the ProMini Rx line is what you have to resolve.

Maybe a switch between Bluetooth's and FTDI adapter's TX lines would do it ?

That could work.