How intelligible is Old Mandarin to the speakers of Mandarin Chinese? If an Old Mandarin Chinese speaker heard a Mandarin Chinese speaker or vice versa, how fluent would the communication be?
I believe the situation is more or less the same in all languages, that the language drifts across generations. Whereas you could easily communicate with Isaac Newton, it would be a little more difficult to do with Shakespeare, and more so with Chaucer. When you get to Richard Lionheart and earlier (say, the times of Beowulf), you can just forget any meaningful exchange of ideas.
As for Mandarin, you could speak perfectly well with late Qing people, although they would still retain tones that are now forgotten. Going back to Cao Xueqin's time (1700s), you would still be able to discern most of the vernacular used, just like you can read 红楼梦 without too much trouble. But you would get progressively lost talking to Su Dongpo and Princess Wencheng of Tang, they would speak a completely different language.
The thing with Chinese, though, is that you could still exchange ideas in writing with these people.
I've searched Youtube for some reconstructed old Mandarin. My background is Jin Dialect and Mandarin, and it sounds no more difficult than Cantonese or Wu dialect to me.
The dialects vary greatly even among modern 官话 of different regions, some can be very different from the standard Mandarin. Usually it takes me one week to one month to understand a different 官话 dialect. The remote rural dialects usually takes longer to grasp. I've seen people struggling with non-native Mandarin dialects for months or years. I've seen people cruising through non-native dialects as if he's in his own backyard. I think it depends.
To put that aside, if you send me a man from Ming dynasty, I think the biggest blockage to communication is this totally unintelligible modern world. As of the language, it would be an issue in the first week, but if we keep working on it, things should get quite clear after a month.
Judging by the tone of the old Mandarin, I think it may sound more intelligible to the ears of the 吴 or 粤 people, but I could be wrong.
This topic is interesting.
Assuming you are referring to Classic Chinese (文言文) as Old Mandarin.
We must be astonished with the intelligence of a person 'speaking' Classic Chinese.
And to my humble (sincere) opinion (wish), Classic Chinese has always been written instead of spoken. (:
This is actually easy as when we look at the literal spelling of the two words in Chinese itself:
文言文 (Classical Chinese) = Written language;
白话文 (Modern Chinese) = Spoken language.