The sun circles the galactic nucleus in the plane of the galaxy, and at pretty much the rotational speed of the interstellar medium at this distance from the nucleus (Remember, in the inner Galaxy, rotation is not Keplerian due to the influence of Dark Matter). Indeed, this solar orbital behavior is often pointed out as one reason why Sol is life-friendly.

Those stars whose orbital plane is inclined to the galactic plane periodically slam into the gassy galactic plane, their magnetospheres interacting with that gas to produce radiation with potential danger to life. Since all stars revolve about the nucleus in quasi-elliptical rosette orbits, they all periodically cross the plane in a N-S direction, but at the sun's distance, the relative velocity between the star and the interstellar medium is minimized (i.e., the sun revolves at approximately the same velocity as the galaxy rotates at this distance from the nucleus.

This is why you often hear about there being a galactic "habitable zone". Supposedly, stars revolving either further or closer to the nucleus are more likely to suffer these radiation events. In addition, stellar penetrations through the galactic plane at high speeds and angles also increases the possibility of high velocity encounters with massive molecular clouds which can trigger comet showers from the stars' own Oort clouds with potentially devastating effects to biologically active planets of those stars.

I personally don't know the full implications of all this for SETI, but it does suggest the sun probably was born in and has always been a member of the Milky Way, not a survivor of some past galactic cannibalism. It doesn't PROVE it, since it is impossible to tell from spectra or orbital characteristics alone which of these populations an individual star belongs to (there are considerable random differences in chemical composition between disc stars of comparable age and gravitational encounters tend to mix the two populations up anyway, making them indistinguishable on a star-by-star basis.).

Statistically, however, it is possible to identify stellar populations from past galaxy encounters, but only by probability. It appears there are stars from other, relict galaxies now in highly inclined elliptical orbits around our galaxy, and these collisions have indeed occurred in the past. Whether or not our sun is one of these stars is not likely, and in any case, is irrelevant. It makes the sun no different, and makes no difference to us, which galaxy it was born in.