How amenable is our own Solar System to radial velocity techniques from exoplanets?

Like others have stated, Jupiter would be the prime indicator. It would take several months to determine the radial movement, several months at least, and well over half an orbit to really suspect an orbiting body as a candidate. Two orbital periods of Jupiter would seem like a good enough time-frame to eliminate other possibilities of the Sun's apparent motion, although I bet after about 7 years, the theories of the Sun having at least one planet would have plenty of support.

But the problem lies with their distance, and the accuracy of their measurements. Farther away, the Sun would have a lessened wobble, if measured in fractions of an arc second, closer, the wobble would be grander. If the technology exists to measure up to tiny micro-fractions of an arc second of movement, and they had the patience to observe our Sun for a long enough time, it would be detectable.

It might be fun to ask a follow up question, in the physics forum, to see how much wobble the Sun has in arc seconds from various distances. They're pretty good at crunching the numbers in that category.

I'm not sure which technique the radial velocity one is.

The resdhift/blueshift technique would probably not work very well.

The wobble method should make exoplanets in our system detectable, although most of the mass orbits at quite a distance, it might take a full year of observations to detect the wobble caused by jupiter. I'm sure there is a maximum distance, where instruments, no matter how precise, would not register a significant change.

The transit method, of course, would work great.

The only planet likely to cause noticeable radial movement in the sun is Jupiter.

So with an orbital period of 12 years an alien would need to study the sun for 24 years to be sure of any movement.

Most of the planets discovered so far have had periods of a day or so.