At first I thought, "no silly, it has to gain matching speed first, what's the point". Then it occurred to me - if we can make something which can survive the impact, we "just" have to place it in the path of the comet and it will be swept with it.
The whole thing would be like something like shooting a bullet at a moving target, but it's an idea.
That hypothetical probe will not look anything like any other space probe before it, but more like an artillery shell. (They can survive pretty damning Gs and still run that little embedded computer, so it's not a completely insane idea, I guess.)
We would also have to detect the interstaller object plenty in advance, so the probe can be launched "comfortably" in a trajectory which will intercept at exactly where the "object" is going to be.
Some quick prompting seems to say a G force of somewhere between 16-160 billion Gs, for a CPU-equivalent object getting hit by a solid object moving at 3I's escape velocity. Compared to a "typical" artillery shell of 10-15 thousand Gs. Not sure you're manufacturing anything that could survive 6-7 orders of magnitude more Gs than an artillery shell.
Of course the G-load would lessen based on how much you sped up to match its speed beforehand, but still, I think you'd need to be pretty much sped up to near the same speed as it before you could remotely possibly survive the impact.
Wow, I clearly didn't think this through. That's brutal.
That leads to another idea - if something more substantial was placed in its path - the resulting debris and gas cloud from the impact could reveal something about the contents of the object.
Or, if it's an alien probe, it would force their hand. :-D We could see some exotic manuevering.
A "solid object". But it's not clear how solid a comet is (or more to the point, this or any interstellar comet). If it were a fuzzball of snow, maybe 20 km across, you could in theory decelerate through it more slowly, maybe using a very large parachute initially, then discarding that for successively smaller parachutes as you approach denser and denser parts of the comet. The EPOXI mission to the Hartley 2 comet was reportedly hit nine times by "snowflakes" coming off the comet, but not damaged (https://www.astronomy.com/space-exploration/spacecraft-sees-...).
The whole thing would be like something like shooting a bullet at a moving target, but it's an idea.
That hypothetical probe will not look anything like any other space probe before it, but more like an artillery shell. (They can survive pretty damning Gs and still run that little embedded computer, so it's not a completely insane idea, I guess.)
We would also have to detect the interstaller object plenty in advance, so the probe can be launched "comfortably" in a trajectory which will intercept at exactly where the "object" is going to be.