If a company accepts a check that says, paid-in-full, does that cover all debt to that company

I don't practice in our state, but I do know that many credit card companies are suing debtors for claiming that a notation of "paid in full" has the legal effect of paying off a debt when the check is for less than the alleged debt.

I know that this strategy will not work in Texas.

It won't work in California either. There may have been a time long ago in common law when it worked but no more.