No, it isn't.
Einstein wrote his 1905 paper in
German, and so the sentence you lifted is
"Zur Zeit t = τ = 0 werde von dem zu dieser Zeit gemeinsamen Koordinatenursprung beider Systeme aus eine Kugelwelle ausgesandt, welche sich im System K mit der Geschwindigkeit V ausbreitet."
and translated as:
"At the time t = τ = 0 , when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. "
. So the use of "Zur Zeit" and "zu dieser Zeit" clearly establish that the sense of "when" in the English translation is only in the sense of meaning "at what time" not "under what circumstances" or "if" as you would have it. Zeit ist Zeit.
That's not to say you can't translate the concept of coordinate time into logic, but since the truth of statements which are frame- and time-dependent are not universally true or false, you can't use predicate logic, but rather first-order logic. The geometry of [post=3198606]post #2[/post] is well-suited for description in the language of first-order logic.
In this language, $$\mathcal{M}$$ is the set of all possible events, a.k.a. "space-time" with a difference operator and a vector-space structure on event differences (thus $$\mathcal{M}$$ is a affine space or principal homogeneous space or torsor over the additive group structure of a vector space). Coordinates are linear functions between $$\mathcal{M}$$ and the set of real numbers, $$\mathbb{R}$$.
So your issue remains: $$ct(P) = ct(Q)$$, $$ct'(P) = ct'(R)$$, $$x(O) = x(P)$$, $$x'(O) > x'(P)$$ and $$ct(R) - x(R) - ct(O) + x(O) = ct(Q) - x(Q) - ct(O) + x(O) = ct'(R) - x'(R) - ct'(O) + x'(O) = ct'(Q) - x'(Q) - ct'(O) + x'(O) = 0$$ is consistent with $$ct(R) > ct(Q)$$ .