Excited helium gas from the colision of alpha particles with beta particles?
This is very much a non-issue. Alpha particles run at great speed, so do beta particles, and as soon as they cool down, they cease to be called alpha and beta particles. When that happens, they may react all right, but there is more to it.

Everything on Earth (look around you! yes, that too) is made of atoms. Helium has greater ionization energy than any other atom. So an alpha particle, as soon as it cools down enough to react, will snatch electrons from whatever else is nearby and become a neutral helium atom. Beta particles (provided they are cooled down, too) are as good as anything else.

But wait, they both cool down by bumping into matter, and matter contains electrons. You will have your helium atoms, but you'll never be able to tell whether the electrons come from beta particles or from something else. Nor does it really matter, after all.