You are correct: Alpha Particles are the same thing has Helium ions with a 2+ charge.
The alpha particle is indeed unstable and will react with almost any material in order to obtain the 2 electrons needed to fill its s orbital.
Alpha particles doesn't react chemically to form an ionic bond, as you are thinking. It merely steals the electrons, via a Coloumbic force. The victim, if you will, is left with a 2+ charge and is said to be ionized (or more likely there are two victims, each with a 1+ charge). That's one reason why alpha particles are called "ionizing" radiation. If the particle that is left with a 2+ charge is in the air, the affect is farely harmless. But alpha particles do severe damage in your body, because ionizing one of the atoms in DNA, an enzyme, an amino acid, a protein, a sugar, or another bioactive chemical will severely alter its reactivity.
So, to answer your question, Helium itself is a noble gas. Alpha particles are not helium atoms, but rather helium nuclei. Compounds with covalent or ionic bonds to helium have not yet been prepared, because elemental Helium is inert.
Another way to answer your question is to consider the opposite. Usually, formation of an ion is stabilizing, right?
Na ---> Na+ (Na+ is more stable)
Cl2 ---> Cl- (Cl- is more stable)
but if you try to do that to a compound that already has a full valence shell, it is destabilizing:
Ag --> Ag+ (Forms a reactive ion)
So alpha particles can't be placed with traditional ions, because they attempt to become stable by ceasing to be ions.
I hope that explains it better.
If alpha particles are going fast enough, they can ionize other matter by colliding with their atomic electrons and just knocking them loose. The kinetic energy of the collision is big enough that the recoiling electron won't be able to form a bound state with the alpha particle and just goes flying off. In this way, an alpha particle can ionize many thousands of molecules as it loses energy while traveling through a material. Alpha particles emitted in nuclear decay may not have such a huge amount of energy and may only be able to ionize a few molecules. The range of a typical alpha particle from nuclear decay is perhaps millimeters -- many are stopped by a sheet of paper. Alpha particles are the most dangerous when they are emitted by radioactive nuclei that are ingested in the body. Then the ions that are produced are inside the body where they can cause chemical damage. Alpha particles are produced in cosmic ray showers and high-energy collisions in accelerator experiments -- again their range in material is short, but we can measure their ability to ionize many molecules along their paths.
(published on 10/22/2007)