Hi, from what I read, an electron gun is only one possible way to make the ions in a TOF spectrometer, possibly not the most usual one.
The process you describe properly does exist, and is the most efficient one in a gas discharge too, which is one other possible ion source in a TOF spectrometer.
An electron arriving with a low energy might be absorbed by the molecule. And an ion can also knock an electron from a molecule, but is far less efficient than an electron for that, because the mass discrepancy makes the energy transfer less efficient than between electrons.