I thought I felt my ears tingle. I haven't been on G2G for a couple of weeks and Harry's post drew me back here. 
James, I see you certainly aren't new to WikiTree, but a fresh and enthusiastic "howdy!" to DNA conversations on the forum.
"Would it be statistically probable for two men to share the same Y Haplogroup but not be linearly or even closely related?"
Short answer: No. Longer answer with sufficient, sciency hedging: It depends.
First, just to get it out of the way--and especially with the nonrecombinant, haploidy Y chromosome--we can track levels of linear descent way back in time. For example, you and I converge at R-P312, but you branch from there to R-Z290 and I branch at R-Z46516 (the two largest subclades under P312). We know we have a shared common ancestor somewhere: the first guy to carry the P312 and CTS12684 polymorphisms. But that puts our ancestor somewhere around 4,800 years ago, give or take.
There are periodic debates about what's meaningful as "genealogical timeframe," and opinions differ. My own take is that the period is defined by the earliest availability of reliable documentation, and that is then--for the most part--dependent upon the time in which a given region adopted inherited surnames.
So you and I share some ancient roots in the British Isles, but we're effectively unrelated genealogically. At least, per the Y chromosome.
Second, it's become more and more tricky to make a definitive statement about a haplogroup designation without doing a little digging.
Back in February 2002, the Y Chromosome Consortium first proposed a nomenclature for "Y-Chromosomal Binary Haplogroups." This was broadly adopted and is the "long-form" naming still maintained by some entities like ISOGG. But...as of that 2002 paper there were a grand total of 243 known Y-SNPs. Not a typo: 243.
Coincidentally, I took my first yDNA-specific test in 2002. And, unsurprisingly, I went over three years before seeing any match.
Eight years later, in 2010, we had over 800 SNPs identified representing 440 branches on the yDNA haplotree. Progress! In 2014, FTDNA and the Genographic Project jointly released their new, combined yDNA haplotree: more than 1,200 branches and more than 6,200 SNPs.
You see where I'm goin' here. This morning, the FTDNA haplotree showed 58,705 defined branches. The explosion started with the first Big Y tests in 2013. With the current iteration Big Y-700, the sequencing looks at about 23.6 million base pairs of the chromosome's approximately 57.2 million (the areas not tested, other than the small pseudoautosomal regions, are densely heterochromatic and full of highly repetitive sequences from which, for now at least, we can't derive any meaning).
As new full-sequencing results come in, more SNPs are identified and more branches split in the haplotree. The older, long-form nomenclature--especially for the basal R haplogroup which accounts for 47% of all the haplotree branches--quickly became pretty much impossible to use. Even as old as our shared P312 is, the long-form name is the unwieldy R1b1a1b1a1a2. FTDNA, in its haplotree, shows me as being five levels deeper than the best resolution in the ISOGG tree.
It simply may no longer be relevant to try to maintain those massively long strings of letters and numerals. Popular now is to use just the deepest identified SNP ("terminal SNP" is, I think, a bit misleading as a term for it because that SNP could branch anew next month), or a hybrid, which I favor, that includes the first level or two from the basal in the older long-form, plus the currently identifying SNP. I usually write mine as being "R1b1-BY35083." That gives the reader a quick clue about where the SNP falls at the 500-foot view.
But there's no longer any single body of governance like the Y Chromosome Consortium to assure consistency in naming the branches...or even in defining the branches. That's where the extra research may come in.
Most of the data are coming in from the FTDNA Big Y test...but not all of it. Entities like YFull and the Y-DNA Warehouse will accept uploads from whole genome sequencing tests and provide a yDNA analysis. So the different haplotrees aren't in lockstep. It may take some digging to figure out if seemingly different information could actually be consistent.
For example, my BY35083 isn't cataloged by YFull, where I've had both my Big Y and WGS results evaluated. Next step higher in branching at FTDNA is BY35076, which also displays seven other associated (and possibly synonymous) SNPs: BY172357, BY35078, BY35081, BY35088, BY51515, FT134692, and FT182955. None of which get a hit at YFull.
At FTDNA, the branch above that is BY22194 plus associated SNPs BY151221 and FT362105. Bingo! A hit on BY22194, with an estimated formation at 1,700 years ago.
The takeaway is that all of the SNPs I mentioned above are valid for that nominally proximate branch on the current haplotree. And the next higher branch, BY22166, has a whopping 61 additional associated SNPs. So the newer naming convention provides brevity and precision, but unfortunately it can also hide a lot of information that needs to be checked before relatedness can be ruled out. Again, somewhat less of an issue for basal haplogroups other than R simply due to the volume. Still a research issue, though.
