There are thousands of engines operating on the wing after considerably more than 60.000 hours. I have no idea what the longest lived engine is before its first shop visit but I am sure it is well in excess of this figure.
I have experience of a CFM 56 in Germany that has been on the wing over 70.000 hours.
I have heard of RRs on B757 that are also well in excess of this number.
I am only guessing, as would you be, but if every take off were made at Max Thrust, I suspect these numbers would be considerably lower.
The answer to the question originally posed, so eloquently and thoroughly answered here, is yes.