We have been using the cheap "PINK" monofilament line that came with our Zebco reels, but since we started dragging Texas rigged plastics across the bottom our lines our constantly breaking. Literally after 7-8 casts we flip it out there and line just snaps. Fishing this route is getting expensive with all the lost hooks and plastics over the last couple weeks. I wondered if we could use a stronger braided line in our cheap Zebco reels to reduce the loss of or bait & hooks?

Replace the line with a better monofilament ...

Those reels would Likely be destroyed by braid

Actually, it is the pick up pin in the reel that will fray and weaken the braid. The answer is still no, don't pit braid on a spin cast reel. The line you have on is probably old and low quality. Try some Trilene XL in 10# - 14# test. It's affordable, manageable and will hold up to moderately heavy cover. Treating the line with a conditioner (KVD L&L if you can) and trolling out any twist after each trip will help keep you up and running. 

Braid is going to chew and spit your Zebco.

Actually, it is the pick up pin in the reel that will fray and weaken the braid. The answer is still no, don't pit braid on a spin cast reel. The line you have on is probably old and low quality. Try some Trilene XL in 10# - 14# test. It's affordable, manageable and will hold up to moderately heavy cover. Treating the line with a conditioner (KVD L&L if you can) and trolling out any twist after each trip will help keep you up and running. 

^^ This.

I would guess that the braid would also eat through the metal plate (not sure what it is called) on top of the spool.  You will notice that mono starts wearing a channel though the soft aluminum after moderate use.  I would think that braid would be much worse. 

Thanks for the help will add a better quality monofilament.