...It would be logical for it to hit the bow torpedo launcher, which is the one thing we know and see is exhausting stuff (if only torpedoes)!
Spock's claim is "Under impulse power she expends fuel like any other vessel." Expending fuel does not mean emitting anything much: nuclear subs expend their fuel in the sense of consuming it, but they definitely don't expend their fuel in the sense of emitting it from a tailpipe! Yet when a nuclear sub expends its fuel in fission, generating power, it does emit neutrons that cannot be readily contained and can in theory be detected from a distance. No known ASW detection method is based on this, but Spock's speculation could be seen as quite analogous to this: sensitive scientific measurement gear, rarely if ever carried, would allow a sub to see another through the neutron flux of the fuel-consuming process, and perhaps a starship to see another through...
...Well, see, that's the problem. Plasma is just "fancy gas", a thin cloud of matter. It doesn't semi-magically leak through the hull, it definitely needs a tailpipe to get out. Yes, it's something plausibly involved when the starship turns its fuel into energy in fusion: a fusion reactor would "expend" deuterium plasma by turning it into helium plasma, say. But where does the helium go? A steady trail of it would completely negate cloaking, and you don't need special instrumentation to see it in space. Other types of plasma from other types of fusion would be even easier to detect.
A cloakship might contain its helium plasma until a suitable moment is found for releasing it. And the moment of firing a torpedo would be suitable indeed! At that moment, Chang's ship reveals her location anyway, as the torpedo glows from the start of its trajectory to the bitter finish. Why not fart helium at the same moment? Perhaps even from the same orifice? Which is where Kirk's torpedo eventually hits...
Timo Saloniemi