Veneer + Invisalign?

My dentist suggested a veneer for my discoloured front tooth but I really want to get Invisalign to correct my overbite. Would it be okay to get the veneer done FIRST (assuming it is done correctly and fully bonded)? I know it's technically ideal to get Invisalign first but is it absolutely necessary? I only ask because I won't be able to afford Invisalign for another year or so and I prefer to get rid of the tooth colour asap. Also, I've already had it bleached to no avail so that isn't an option