Short version : not bond, maybe interact.
Would these particles bond or interact with atoms?
Atoms must travel at a velocity lower than light speed in all reference frames.
Tachyons must travel at a velocity faster than light speed in all reference frames.
There is no way both types of particles could bond as they cannot ever co-move in any meaningful way. From the perspective of an e.g. electron (in the electron's rest frame) the tachyon would always be moving faster than the speed of light. How cold the electron be bonded to such a thing ?
By interactions I mean bonding with atoms and dragging them backwards in time or simply destroying or kicking out electrons, protons or neutrons and/or replacing them.
Ordinary (non-tachyon) matter has to stay at a velocity below the speed of light to be "seen" by other ordinary matter as behaving like ordinary matter. A tachyon can never do that, so it can never "look like" ordinary matter.
There are any number of other complications. For example, tachyon matter would have to have imaginary mass. That is to say it's mass is neither positive ("the usual thing") or negative (so called "exotic matter") but imaginary (a scalar multiplied by the square root of -1). There's no way to apply e.g. conservation of momentum if you try and replace an electron in an atom with a tachyon in an atom because all of a sudden you have an atom with an imaginary mass component which makes no sense at all.
The best you might manage...
Tachyons might (arguably) interact (in the sense of scattering) with ordinary matter due to e.g. electromagnetic effects. I'm not convinced this is viable, but can't locate a paper that discusses this from a source I could give any credence. This would mean that a tachyon and electron might deflect each other in some way. However this still causes problems with conservation of momentum because of the mixing of imaginary mass and normal mass (and hence imaginary valued momentum and normal valued momentum).
Such an interaction might (we're in deep handwavy territory here) create a hybrid state that isn't a pure tachyon or a pure-non-tachyon, but a thing with both an imaginary mass component and a real mass component. This doesn't really make any sense in physics. Energy and momentum for such a particle would have a complex value and it's really hard to see how such a particle's dynamics would operate, if at all.
Note that if you want to preserve the universe in a state remotely like the one we have, such an interaction would have to be extremely rare. It would essentially have to be undetectable because it's so rare an occurrence - that level of unlikeliness. If it happened with any frequency (even in e.g. high energy particle physics labs) it would be incredibly obvious because the effects would be quite obvious (i.e. "physics is completely broken" obvious).