Short answer is no.
There are vet bringbacks that didn't get stamped. Privately owned guns brought into the country by US citizens and a few other odd cases where guns legally came into the country without getting import marks. As long as it's not stolen, illegally modified or otherwise a flat out no-no, you can have whatever you can afford.
Last and very important point. The law requires licensed importers to mark firearms, it doesn't require private parties to audit the history of every gun we buy. Buy the rifle. Keep the receipt to show you bought it legally. Enjoy your new prize.