It depends. First, what do you mean by "any aerobic benefit"? Second, what kind of athlete are we talking about?
As far as we know, most of local aerobic adaptations to a short, easy bout of exercise are minimal. As for central aerobic adaptations, a two-mile run will have some effect. If you are very fit, the effect will be minimal, but all exercise has a minimal effect on the highly trained. They've reached a level where only VERY hard exercise will continue to produce adaptations. If you're a couch potato, 2 miles is a workout. (I'm going to assume we're only talking about easy runs here, as a hard 2-miler will have "some effect" for just about everyone.) Also, it's crucial to keep in mind that we simply do not know everything that happens in the body in response to exercise.
As for recovery, there are a lot of misconceptions about "recovery running." You are definitely not "flushing out lactic acid" or other waste products. That happens automatically and very fast after hard efforts. We do know, however, that after hard efforts, resting blood lactate is elevated (not because it hasn't "flushed" but because you produce more at rest when you're fatigued). Short, easy runs can more quickly bring blood lactate down to baseline, but it's unknown whether this kind of suppression indicates faster recovery. There is also the benefit of increasing GH hormone secretion so you're in an anabolic window for a larger percentage of the day (though 2-miles is short for this effect). This can also help with glycogen restoration and appetite suppression (not necessarily incompatible). Light runs also have an analgesic effect, likely reducing soreness even if the underlying damage isn't fixed any sooner.
My personal theory on recovery running is that it's valuable for maintaining full range of motion while tissue is being repaired after harder efforts.