They might, and they might not. A 30-06 with 180 loads is not the heaviest of recoilers, but they do kick.
I don't advocate using those cheaper rings on anything but rimfire rifles, so you can imagine that I wouldn't advocate them on use on a .30-06.
Yes, they may be cheap (in price) and easy to mount, but consider the possible (or likely) chance of them breaking, getting new mounts, and taking the time to mount the new scope, and spend the money on ammo to sight it in - wouldn't it be better to just spend a little extra money and get a much better product and get it done right the first time? (That's a yes! :grin: )
Zachary