I shoot with flash, and manly do so because I could not get my blended stuff to look like Smooth's.
Some things to keep in mind.
That unit is too heavy to hand hold, so you will need to move your tripod and power cord every shot. As you do, the shadows will change to reflect the new position of the light. This can lead to odd effects and blending errors as the "shapes" of things change by virtue of highlight and shadow changes. Not every room will allow you to put the light were you would like. Dining rooms and bedrooms in particular will be a challenge for placing your light stand.
The inverse square law in a big issue when using a flash like this. Basically, as the distance from a point source of light doubles, the power of the light is cut in half. So if your flash is 20ft from a wall, and you are getting a reading of f8, your ceiling that is only 2.5ft above your flash will be reading f32!
Also, if you are not positioned dead center in a room, one wall will receive more light then another.
That is a big problem in tight spaces like the entry way of this home.
The only way I have found to deal with that is blending and touch up of the panos in photoshop, post blend and stitch.
I use a portable battery powered flash made by Norman, like this one.
Some others are here.
I made a defuser for my flash head, and hold it over the top of my camera to so that the lighting is consistent from shot to shot. Be prepared to reshoot if you get the flash to far forward and you can see it in the shot.
Not trying to be a kill joy, I like the way my panos look using flash, and for the cost of that you should try it.
ETA And don't forget about reflections. You will either have a light stand and flash to contended with, or you will be in the shot if you handhold the flash.