No, because this statement is wrong. You cannot make sense of the left hand side as an operator on a Hilbert space, since $|O(x)\rangle$ is not a normalizable state in radial quantization if $x$ is not inside unit sphere. Furthermore, $|\tilde O(x)\rangle$ cannot be defined as a state either, for the same reason.
The left hand side makes sense as an operation you can do to three-point functions. However, it yields Euclidean conformal partial waves, while the right hand-side (which needs to be written more carefully) yields conformal blocks. Refer to this paper.
You can write and prove something like this in Lorentzian signature, in several ways, but it is more subtle.