If by "capture" you mean the electron joins the proton in a new Hydrogen atom, that can certainly happen. But it only happens at extremely low energies. Just a handful of eV, no more. And the energies and directions of the two particles need to be just right.
But if you're talking about some kind of absorbsion going on, things are different.
Let's say you shoot an electron directly at a proton, so that they collide. They do this at the HERA lab. It's not going to be like two billiard balls colliding, because the proton is really made of smaller things. At sufficient energies, the electron is going to collide with one of the quarks or gluons that the proton is made of, if it collides with anything at all.
There have been observations at HERA of electrons colliding with something OTHER THAN a quark or gluon. Quarks and gluons have "color" attributes, but sometimes you see an electron interacting with something "colorless" within the proton. The electron appears to be "scattered" when this happens. I have no clue what's going on when that happens.
Sometimes, what happens in this kind of collision is that the proton and electron reassemble into a neutron and a neutrino. A heck of a lot of energy gets released. Sometimes, you wind up with an electron again, plus a lot of hadronic junk.
The coolest observations, however, are when an electron dives into the interior of a proton, and gets reflected straight back out the way it came. As if there was a mirror deep inside a proton. This seems to contradict the Standard Model (which would require such a reflecting object to be very very massive and also have very strong interactions with leptons), but further analysis is required before any conclusions are drawn. It may well be that the collision of an electron with a quark changes the nature of the quark so that behaves this way (some call that hypothetical creature a "lepto-quark"). Or it could be something not yet dreamt of in our philosophy.
