What are the chances of...

[razark]

Is that assumption correct?

Sort of correct. If you're not focusing on an object (ship or asteroid), it will pass through the atmosphere with no braking.

[KerikBalm]

or despawn....

But you can have it aerocapture on one pass, and then once its 2.5km away from the active vessel, its orbit becomes "meta-stable" as long as the PE is above the despawn height.

When I say meta stable, I mean its stable for as long as you don't focus on it while it is in the atmosphere.

As for the asteroids shown to be orbiting, but are actually on escape trajectories - I've had the same thing, but also with some vessels, where the game can't quite decide what their orbit will be.

The reason for this is that the SOI is not quite as far out as the highest sub-escape velocity perapsis.

If there was just 1 body, it would be in the orbit shown (while when it reaches escape velocity, its trajectory would look just like an escape trajectory from Kerbin's Sun - no SOI transition, but still no more elipse), but the apoapsis is beyond the SOI for the patched conics

[Rolanvorxariat]

oh the first asteroid redirect mission i did, there was a asteroid i called Joe which would intercept kerbin witha a peri of 400 km. I was originally shotting for a a c-class asteroid i nicknamed "Melvin" That had barely any inclination, but when "Joe" entered kerbin's sphere of influence, it was going on a flyby trajectory of the mun witha peri of 97 km, which would slam it into kerbin. immediately changed my plans for joe out of necessity, and on a tight scheduel because it would leave the mun in t-15 days, and my eve mission would enter eve's sphere of influence for serobraking in 16 days. fortunately, i got both done.