It's actually way up in the air, but it's possible. Though I would like to add some food for thought. Originally, there was plans for one to be able to import their character from Arena to Daggerfall. Obviously that didn't happen, but it's something to consider.
While I personally like the idea of the eternal champion being stepped on by a giant robot I have to point out in the daggerfall chronicles(offical guide written by bethesda) there are two birthdays one for each champion.
One way of getting around that would be to say the warp had more of an effect than was seen and the eternal champion was born on both dates. So theorically you could have Jauffre be the eternal champion but not the daggerfall hero who is also the eternal champion. but for simplicitys sake lets go with two diffrent people.