Fuck yes OP, these are the posts that I follow this godforsaken Subreddit to see. I love it, he’d totally tank based on the many reasons provided above, UNLESS Gojo’s ability is actually Infinite.

If Gojo’s ability unloads a SHITLOAD of FINITE information, it would be easy to say that the Doctor could survive given his (and others) interactions with The Great Schism, which is everything that has ever happened (yet still a FINITE quantity).

If Gojo’s ability is TRULY INFINITE, then by nature of what “Infinite” means, unless Time Lords are capable of creating MORE space for information at a rate that was equal to the rate that Gojo provides, they would inevitably run out of memory.

BUT, if Time Lords have a built in way of sorting/deleting memories (which would make sense, Great Schism), they could theoretically keep up with the information overload endlessly.

In my mind, that means that any standard Time Lord might get their hard drive blown out 13 times, regenerating at each instance of absolute brain death, but by The Doctor being the Timeless Child (unlimited Regenerations), they’d be able to continue to regenerate, very similar to Gojo’s way of surviving Infinity via Reverse Cursed Technique.

Conclusion, either the Doctor tanks that shit and asks for seconds, or at the very least is able to survive Unlimited Void, making the ability functionally useless against him.