We have no direct evidence for proto-Indo-European (PIE) we simply infer its possible existence from the similarities between other reconstructed languages, such as proto Celtic and proto Germanic. The most popular theory assumes that PIE (either one language or a group of languages with close connexions) evolved somewhere in the Central Asian Steppes and spread from there - with the branches becoming distinct during the gradual migration process. So at least according to the mainstream belief of philology, based on the evidence they have and their methods of reconstructing proposed historical languages - the answer would be 'NO'.
PIE diverged in to mutually unintelligible dialects or separate languages during the migration periods, with varying levels of influence exerted by existing languages it met along the way.
The are however some elements which remained very stable, such as words which were used on an everyday basis and which therefore allow us to assume the existence of a common ancestor language. The prime example being the word 'water' which was what allowed Hittite to be identified as an Indo-European language despite being written in a Semitic script.
So, whilst the languages would not have been mutually intelligible, it's possible that certain very common, everyday terms would have had a high degree of mutual intelligibility for a very long time after the migrations split peoples assunder. Names for family members such as father or mother or sister, words for milk, bread, water, words for domestic animals etc. In much the same way that English and Frisian have these areas of similarity despite being very different when discussing more complex or obscure subjects.
Edit - should make clear this theory assumes migration of actual people, and also migration of culture, that is to say people adopting language through cultural exchange (marriage, conquest, trade, alliances, technology etc.)
http://www.utexas.edu/cola/centers/lrc/general/IE.html
I recommend you ask this in /r/linguistics
Good question. Languages diverge and become mutually unintelligible when its dialects are geographically separated and enough time passes (roughly 500-1000 years). So the question is, did the Indo-European languages spread far enough for them to reach opposite ends of Europe and South Asia before they'd diverged? The two most plausible models of how Indo-European languages originated and spread, the Kurgan hypothesis and the Anatolian hypothesis, imply that it dispersed at very different rates. In fact (and here I summon the wrath of the linguists), this was the idea behind a controversial Nature paper that brought the Anatolian hypothesis back from the dead ten years ago. It's fair to say though that, that aside, Indo-Europeanists have paid far less attention to the spread of Indo-European than to pinpointing where Proto-Indo-European (PIE) came from, so answering this question involves a lot of extrapolation and not a lot of hard data.
The Anatolian hypothesis is tied very closely to a specific mechanism of dispersal: the spread of farming and an accompanying mass migration of farmers to the Near East into Europe in the Neolithic. This was a very slow process. From its epicentre in the Near East 9500 years ago, it took over a thousand years for farming to just to get through Anatolia and hop over the Bosporus, and it didn't reach the Atlantic fringe of Europe (e.g. Brittany) until three or five thousand years ago. Assuming the first farmers of Europe took their language with them, it had plenty of time to diversify. The spread of farming happened in fits and starts, so certain rapid dispersals, like the spread of the LBK farming culture across central Europe, may have left large regions where a single language or a collection of mutually intelligible dialects was spoken, but overall the process was too slow for Indo-European speakers on one end of the continent to understand those on the other.
The Kurgan hypothesis is much muggier on how PIE got out of its steppe homeland. The general idea is basically that highly mobile PIE-speakers "infiltrated" the old sedentary societies of Europe in a time of crisis, setting themselves up as local patrons and their language as the prestige dialect. One of its main problems in my view is that something like that is almost impossible to see in the archaeological record, so we can't put any dates on it directly, but conceivably this could have happened very quickly, maybe in a few generations. This would have created a zone of mutually intelligibly as far as the initial PIE-speakers and their immediate descendants migrated, and perhaps its utility as a long distance lingua franca is another reason it eventually supplanted indigenous Pre-Indo-European languages. But you specifically asked about Brittany and India and, as it happens, the Kurgan hypothesis puts both of them as receiving Indo-European in separate dispersals well after the initial spread of PIE: Brittany with the Celts; India (and the Anatolian hypothesis agrees on this by the way) with the Indo-Iranian speaking 'Aryans'. These spread languages that had already long diverged from each other.
So, if you buy the Kurgan hypothesis there's a possibility that there was once a fairly large area where PIE was understood (the Pontic steppe, much of eastern Europe and Anatolia) but under either hypothesis there was never a time when people from Brittany and India could talk to each other in their own languages. I should stress though that both of these models, though they're best we have, have serious problems and an overriding lack of data to back them up. Personally I don't believe for a minute that things played out in either of the ways I've described above, but I don't have a better explanation!