@Matthew-Champion The answer to the question in the title is yes. Generally the particles coming out of an interaction are entangled in some way at least until one of them interacts with something else (and note that a measurement is always a case of “interacts with something else”).
However, that “yes” answer does not imply what you’re asking in the body because entanglement doesn’t work the way you’re thinking. Changing one part of an entangled system (in this case, manipulating the atom after the emission) has no causal effect on the other parts of the system (in this case, the emitted photon).
There are two possibilities here. One is that we measure the wavelength (energy, frequency, they’re all related) of the photon first. This interaction breaks the entanglement so nothing we do to the atom later changes the photon energy from the value we’ve measured. The other possibility is that we interact with the atom first, breaking the entanglement, and then we measure the wavelength of the photon. Either way, we get one measurement of the photon and its wavelength is what we measure.