I dont see a problem with fixture at all as I have buit
DIY light for specific appilcation including MH. All youmay have to do is replace common household/office bulbs with more specifically engineered tank bulbs such as 10Kday, 12K day, act 03 7100K or 50/50 combo (if avail), etc thru online hobby store. Wether these specific bulbs for reef tank are avail at HD, I am not sure but I am sure you can find specific onlight light bulb site where you may find exact same bulbs (even if different mfr, it's ok when wattage, style and color temp are the same, KELVIN)) as ones sold at online hobbystore/
LFS for less money.
I dont see a problem with 4 x 24W=96W total output with proper bulbs for most corals (soft,
LPS, mush, polyps) in 20G tank but probably not enough for Tridacna Clams though.
If your Shoplight can be wired to 2 or 4 different switches, it is even better (can at least put bulbs on timer to simulate the sun. I think timer system is better for all the inhabitants rather than expose them to 96W or whatever it maybe in the matter of click of a switch.
I have had certtain fishes die of heart attack when exposed to sudden bright light after being shipped for day or two in the total darkness.
Hope this helped a bit.