Can I replace a ceiling fan with recessed lighting and a dimmer switch without rewiring the wall?

We’re turning the upstairs room into a TV room that used to belong to our teenager. There’s a ceiling fan with a light in the middle of the room.

I’m thinking of taking out the ceiling fan and light to put in 6-8 LED recessed lights instead. Do you think I can use the power wire that was connected to the fan for the recessed lighting? And I’d like to switch to a dimmer switch. Do you think this plan will work without having to install a new gang box and wiring down the wall?