If two people share a thought influenced by their shared experiences, would this
No. At least, not if by "telepathy," you mean what most people mean. Usually when people talk about telepathy, what they have in mind is one person's thoughts influencing another person's thoughts without usual means of influence such as speaking, telephoning, etc. What you've described is a case of "common cause." It's not a matter of one person's thoughts influencing another person's. It's a matter of a common stimulus influencing each person's thoughts.
To give a clearer example: suppose you and I are, as it happens, both watching the same TV program, though in different cities. An image of a mushroom cloud appears onscreen and we both think of Hiroshima. That's not telepathy. Nor would it be telepathy if the two of us had also once met and talked about the history of the atomic bomb.