Summarising the discussion above: Any symplectic structure on $\mathbb{C}P^2$ which admits an embedded sphere of self-intersection $+1$ is standard by a theorem of McDuff. Gromov's original paper shows that such a sphere moreover must be smoothly unknotted, i.e.~isotopic to the standard line at infinity. Thus: If we take $S \subset \mathbb{C}P^2$ a smooth sphere whose complement is not is simply connected, no tamed almost complex structure exists for which $S$ is pseudoholomorphic.
Nikolaki
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