Absolutely! I've been 'lucky' twice, though I put it down to a lot of detective work as well as quite a bit of luck
My paternal great grandmother was illegitimate - born 1870 but no father's name on her birth certificate. Her mother would only have been about 14 when she was conceived and the grandparents passed my gt grandmother off as theirs on the 1871 census. I'd resigned myself to never knowing who her father was - until I did my DNA test and got a match with a lady in the USA, who was as determined as I was to find our - rather strong (46 cMs) - connection. The connection was actually with her husband's side.
We kept chipping away, even though she didn't have a tree on Ancestry, but we were making no progress until I checked out our shared matches (I was new to this at the time - I look at the shared matches as a matter of course now). This 2nd match had one chap - and only one - in England and. long story short (and it did take a few months!), that name turned out to be the 3-way connection. My natural great grandfather was more or less the same age as my gt grandmother; lived a few hundred yards up the road from her on the 1871 census - and emigrated with his parents and siblings to the USA soon after!! Since then about 4 or 5 further matches have arisen from the same US family - and most of them also match with my brother and my niece.
My second discovery was of a similar nature (53 cMs) but concerned my maternal great grandfather who was born 3 years after the death of his mother's first husband, and 3 years before her marriage to her second husband. Again, I'd pretty much given up trying to find his father. Again, it was the American lady's husband who was the link and again it took some finding. Eventually a surname she gave me for one of her husband's US ancestors triggered something in my head - not that I had that name in my tree but it sounded very much like a west yorkshire surname, and that's where my gt grandfather lived! From little acorns, and all that!! The US family hadn't even researched their tree back to England but had a vague inkling that family stories said that's where that line might have come from. Again, later additional matches proved to confirm it even more - and,yes, their family also emigrated to the US soon after my gt grandfather was born.
So, luck - yes - but, make no mistake, you'd have to be very, very lucky indeed if you just sit back and wait for the matches to come to you. They almost certainly won't. Keep chipping away (politely) give people access to your tree if its private and just keep the 'conversation' going.
I suppose that matches further back in time may prove more difficult to establish, especially if there's no census to help verify where they were living at the time, but I do currently have a third one (23.1 cMs)I'm working on and she was a 3xgreat grandmother born in 1805!!
Jill