It honestly depends on the scope you're using as the objective bell adapters are actually different thicknesses near the bottom. In most cases, 1/4" is adequate. If you're running a scope mount/rings with a lot of built-in MOA, you'll need more clearance because the charlie will be angled down at your barrel/handguard.
If you're running a handguard with a picatinny rail, however, I'd just recommend buying a rail-mounted Charlie. That way clearance won't be an issue. They're a little faster to take on and off, and as long as the rail is plumb/level with the optic, cant won't be an issue (you have to level the charlie adapter to your reticle when you first mount it.)
I'm out of the shop at the moment and don't have an optic on hand, but as soon as I have a number for you I'll give you a definitive answer.