It will indeed. I got similar LED dome lights. Simple install btw.
Just pull the dome off of the ceiling. REALLY pull, it's held up there with metal clips and will make a loud metallic "ping" sound when they come loose. Then you can pull the lights out through of the back of their housing to replace them.
Alternatively, you can use a pocket knife or flat-head screw driver to pry the lenses off of the dome and just pull the stock bulbs out of their housing that way (this is how I did it). Don't worry about breaking the lenses as they are flexible, but take your time.
Whichever floats your boat.
Here's the link to the ones I bought in case you aren't sold on the ones you've found. They are BRIGHT. As in "daylight-in-your-car-at-night" bright. 2005-2014 Ford Mustang Dome & Map Light LED Upgrade (W/built in Resistor) Double the light