Well if you want to hand wave stuff for a story, sure. The issue with the beacon is a few fold though. So, let’s say they use something close to the speed of light to communicate like a laser and there happens to be no obstructions and the beam is so narrow and powerful it just works. Being even a few light years away just isn’t accurate enough to know exactly where something is going to be in space. Sure, if it travels in an exact straight line (so it’s not near any massive bodies) there’s likely to be some sort of drift, even slightly angular. That’s going to translate into likely at least kilometers in the 10k range between the time it takes the data to be known vs. how many years have already passed from that last bit of data.

Sure though, take away any need for inertia or fuel and yeah, they can just stop somewhere, figure it out and go again and grab it or better yet there’s just some technobabble thing that can instantaneously keep Sol updated in near real-time but also the ship coming to get it. That’s just plot devices for a story though and an author can hand wave away anything they want, so there’s no need to say that if we just talked about a problem in advance, we would just figure it out and make it happen because that only needs to be done in some made-up fantasy if that’s what the author wants to do.