Do you need to have the SRAM Red Etap shifters on a road bike to use the blip box or can you run a road bike with just the blip box and blips?

You do NOT need SRAM Red STI shifters on a bike to use the blip box. Any TT bike with SRAM has only blips and/or clicks, but does not have STIs. However, I am wondering, what you are going to use instead of STIs?

So I have a road bike set up with mechanical gearing and taken my blip box set up off my TT bike so was hoping to just change it over without needing to buy the shifters?

You want to „get rid“ of the entire mechanical groupset of you road bike and install the eTAP groupset of your TT bike on the road bike?
Technically, that works. However, you still need brake levers (TT brake levers do not fit a standard road handlebar).
You could also buy a pair of eTAP compatible STI levers and don‘t need the blip box at all…