Unless you have a transaction tax, this isn't really so. As a contrived example, company A buys thing from company B and sells it to company C, who sells it to company B, all at the same price. There's no profit anywhere in this system (so no tax), but there is economic activity (so, GDP).
Many countries charge a flat x% on revenue (not profit). There is also sales tax (VAT) which has to be eventually paid off by the final consumer. There also other taxes derived from the activity (real estate, employees, etc.). So hardly any company can "operate" without paying any taxes.
Corporate income tax is usually a small slice of the overall taxation of a country.
What GDP measures (and what I meant) is the visible part of the economy that the government has knowledge of; and therefore can (not necessarily do) tax.