Answer
Yes, hydrogen will react with different mass of chlorine isotopes. No, this does not conflict with the law of definite proportions.
Work Step by Step
One atom of hydrogen will react with one atom of chlorine regardless of the isotope so both isotopes will have different mass of chlorine that reacts with 1 g of hydrogen.
This does not conflict with the law of definite proportion because the law refers to atomic ratios, not atomic masses.