No. It seems that most Death Eaters have to be fully qualified wizards before joining (with the exception of Draco Malfoy). This means that Theodore would have had to finish his education and 'come of age' before signing up, which he didn't get a chance to do before Voldemort was defeated by Harry Potter. There is a possibility that Nott would have joined the ranks of Death Eater, taking after his father. If I had to guess, I'd say Theodore would have become a Death Eater, given enough time. It seems inevitable given his family history.