How well would the average 21st century person fare in academia in the 19th century? Would the average intelligence of a college graduate in an associated field be that of a 19th century Masters or PhD?

Your question is a bit unclear to me. Are you asking about the intelligence of a college grad, then versus now? Or are you asking about their knowledge?

We have no particular reason to suppose that a modern college grad would be more intelligent than his peers from the 19th century. Flynn Effect notwithstanding. If there's been an increase in average IQ at the population level, it's probably due to better nutrition having raised the lowest parts of the curve. Intelligence at the upper end has not changed so far as we know. And universities are self-selecting environments for the upper end, they don't represent population averages anyway. I see no reason to believe that a modern university grad has a higher IQ than one from the 19th century.

If you’re asking about knowledge, well obviously a 21st century graduate has access to knowledge the 19th century guy didn’t. Whether that would be enough to convince others of your brilliance is questionable. Having access to 21st century factoids isn’t very impressive unless you can prove them, otherwise why should anyone believe you? For the average grad, it’s much easier to remember the result than to duplicate the long chain of reasoning that led to it. But the result is arbitrary and unconvincing without the support.

Probably would depend on your particular field of academia as well. Science is more empirical, so even if you can’t provide a convincing argument you can still rub people’s noses in the results and say “look, it works”. It’s different in the humanities, where arguments may rest on books that haven’t yet been written. The whole body of work on which your analysis depends doesn’t exist.

I suppose it’s possible to impress with trivia too. Perhaps you remember where some ancient undiscovered city is buried and you say “dig here”. Or make some money predicting the outcome of sports events. But that’s just magical information-from-the-future stuff, nothing very remarkable about it.