My first question to you here is- how many generations back do you think this genetic connection might be? Because once you've gotten 5 generations back (great-great-great grandparents), there's a decent chance that you may not have inherited any DNA from an ancestor. However, of course, this doesn't mean you and another person aren't family! It just means this particular person's DNA (or at least, a notable portion of it) didn't manage to make it to both of you. And when you think about how many more people would've married into the family within that (5 generation) time, it's totally understandable.
Now for the real science. Essentially, once you get down to 2cm, you're fairly likely to be looking at ANCIENT dna. As in, everyone-ultimately-came-from-Africa or Ghengis-Khan-had-how-many-kids level ancient. So basically, not something you should even remotely rely on when doing genealogical research. You've probably heard the 'fun fact' that all humans share 99% of their DNA. While that's not an exact, universally accurate statistic, there's a kernal of truth to the general idea... which is why most DNA companies have a 5-10cm cutoff. In fact, GED match has been pretty notorious for giving false positives, simply because it allows its users to lower their threshold so much. Most companies have good reason for not doing that! Some people have actually done little experiments with GED: once they lower their threshold to 2cm, they suddenly become 'related' to a fifth or so of the site's users!
In sum--- No, it is not a significant relationship, nor telling evidence of one. BUT: as I explained in my first paragraph, you and this person might very well be family, even if your DNA doesn't match up as such. So this is certainly not a reason to give up on the possibility of a relationship! But perhaps it's time to take a step back from DNA and focus on records/research. Good luck to the both of you
