It might help a bit, as you mentioned that Voyager is currently going about ~17km/s, so nearly 0.005% c, so it's already nearly 1/200th of the way there to our target of 1% c.

But then you're at a velocity so far beyond the escape velocity of most bodies you'd need to be skirting stars, then black holes to get anything more, and that's where it dives straight into "sci-fi" rather than anything even close to theoretically possible. How far away even if a body like that? Will this "probe" even survive such an encounter?

So even with that sort of slingshot it's well within the "Estimate Rough Error" of my intial numbers. They're "order of magnitude back-of-the-envelope calculations" of spherical spaceships in an already unrealistically biased to make the numbers smaller vacuum (just reaction mass, no thought of any mass of the engine or spacecraft body itself, or containing the reaction mass itself, or anything like that).

I probably should have stated my assumptions - in that "Can we accelerate a probe" I assumed that:

- The "probe" is a significant size - if we define a "probe" as a "Single Ion" then we already do that at CERN and similar pretty regularly - 1kg was my assumption of "Useful Probe Mass"

- "We" - in that "humans" as we know them today, preferably in the realisic age of civilizations as we know them, or even better within the lifetime of a currently living human.

Also there's different levels of "theoretical". VASIMIR has only ever been shown in lab settings, so still "theoretical" as a propulsion technology. something like Project Orion is "theoretical" in that it's never been built, but likely just an engineering effort. IKAROS showed solar sails are "possible", but so many orders of magnitude away from what would be required it'll still be a significant engineering and development effort to even show the same idea at the required scale is possible. Things like lasers as remote energy sources haven't really got off the drawing board. And then at the extreme we have "theoretical" ideas like fusion rockets, which are more "Not show to be /impossible/" rather than anything we could even start at really building today.

And each step along that "further out into theory" path means more risks, and more changes that method is shown to be less useful than really desired.

Space sails are super low thrust though, even lower than my VASIMIR example - so will take even longer to reach the desired speed - though they have the advantage of not having to carry the complex and heavy engine I ignored that in the rough estimates anyway.

So by the time they're theoretically close to the desired speed they'll be on the other side of the galaxy at least, even if it took millions of years to get there at the much slower average speed.