“Could” is actually better because it expresses more uncertainty. Since you said “whether”, you have made things uncertain. That’s why “could” is better than “can”.

‘Could’ is possible but changes the meaning in an important way. Whether he was doomed, you couldn’t tell. (You are making the determination of his status in the past) Whether he was doomed, you can’t tell. (You are making the determination now) Replacing ‘not’ with ‘never’ extends the time period. You can never tell. (Now, and in the future) You could never tell. (In the past, and after that time in the past)

"could" is often used as a past version of "can". Given that "was doomed" appears like we are talking about the past, I would prefer "could".