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I wasn't familiar with the Pioneer Effect, per se, until you mentioned it, though I think I remember seeing something along these lines some time ago. It obviously didn't register with me, however.

I did a Google and found an interesting web site with an abstract of an AAS presentation by two researchers, one from JPL and the other from Los Alamos. This quote kinda puts a damper on the subject, at first glance:

In the absence of any physical theory that predicts such an acceleration, the primary candidate remains systematic error generated by spacecraft systems.

But then they turn around and say:

However, neither we nor anyone else has been able to find a viable spacecraft systematic that is both large enough and constant enough to explain the anomaly.

Which flips it right back to looking like a possibility.

OK. So what's the significance to the discussion of near Earth or Earth impacting objects? Well, that appears to be part of the paper, too:

We show that the Pioneer anomaly, interpreted as a physical effect external to the spacecraft, can have profound implications for LP comet orbits.

<snip>

In addition, it eliminates all hyperbolic orbits. The Oort cloud becomes a narrow shell of comets at about 2500 AU with a thickness of about 400 AU.

<snip>

In these models, comets entering the solar system on interstellar orbits become nearly parabolic on their first pass, as observed, and then undergo further evolution by drag and planetary perturbations. Large effects on short period comets such as Halley and Encke are avoided by assuming a hole in the resisting medium inside 10 or 20 AU, consistent with limited Pioneer data analysis in this region.

I'm going to continue to Google to see if I can find more. But it's an interesting question.