Of course those pursuers wouldn't treat it that as unforgivable crime and throw you into Azkaban. They would only treat the arrested contestant as a tourist that coincidentally encountered a bowtruckle and generously donated it to the museum. Therefore, even if he was caught, there will only be a flash of light and his memories erased.
However, this may seem like a light punishment but is is extremely disastrous. The flash of the pursuant will erase whatever experiences the contestant had in the world as well. Therefore, if Sheyan received that spell, Hagrid wouldn't recognize him, even the items acquired from the troll would be erased.....when that time comes, completing the mission will be tough and the completion rate would be horrendous.