Bag and strap felting question

I’m adapting the Booga Bag pattern to have a flap over the top (weather reasons because of where I live) and was planning on picking up stitches to knit a strap from one side to the other.

My question: can I felt the bag with the strap attached, or do I have to knit the strap onto the bag after felting?

I always felt with the handle already attached.