you will be fine. it will have a bit more of a boomy low end, but i doubt you will really notice anything.
if you are keen, you could experiment yourself and use the box you got, and then get some closed cell foam (like they use in electronics packaging - or some expandable foam) cut it into a section that will fit in your box (after your measure it of course) and see what you can tell - if any.
id prolly drive around with it in 2.0cf for a week, then change it to 1.5 for a week, then 1.0 for a week, and make sure you listen to all the same songs a few times with every change of box volume. try different kinds of music, from rap to rock ect.
but i dont think you will notice anything wrong with the idq in 2.0cf. my IDQs ive tried in 1.2cf, 2.0@35, infinite baffle, and 1.8. they all sounded great (i had a single idq12 and two idq 15's thus far)
let me know what you decide to do!