Can helium and chlorine combine to form an ionic compound?

No, it rarely bonds with other elements, and if it does the only one it would bond with would be Fluorine, which they have done before, and if and when it bonds with fluorine and/or oxygen, it would form a covalent bond.

If you were to to take either of the two elements and try to perform an chemical reaction, when you find the electro negativity (ΔEn, which is equal to En2-En1) you will notice that it will fall below 0.5 or greater than 1.7 , which will be a covalent bond (an ionic bond will be between 0.5 and 1.7).