Hi John and welcome. Absolutely not. Cheers, stay safe and enjoy!

Hi John, while tracer rounds do introduce elements that potentially lead to increased barrel wear, the accurate measure of this impact depends largely on other contributing factors such as barrel type, maintenance practices, and usage.
The general consensus is they cause more wear (compared to most rounds) on the barrel but they don't "damage" them.
Stay safe & have a great day!

No

You can buuuuut....
However, it's essential to keep in mind that tracer rounds also have some drawbacks, such as giving away the shooter's position, potential for increased barrel wear, and the risk of starting fires due to the burning pyrotechnic compounds.