Crates do not appear to work with Quark's Dropoff button, which allows players to automatically deposit their inventory into storage. Adding the ability to use this button would be awesome.

Tested with:
Forge 2705
Quark 1.4-125
Better Crates 1.0.3

The compatibility if done via support for IItemHandler would also open automatic interoperability with other mods that want to prevent nesting of container-like objects. Maybe a custom ItemBlock that implements the IItemHandler capability instead of the vanilla version for your crate blocks.

For use "Dropoff" button you need change Quark config.
.minecraft/config/quark.cfg -> "chest buttons" -> S:"Dropoff Enabled Blocks" ->
Add "bettercrates:wooden_crate" for Wooden Crate.
Same with iron/copper/etc..

I will consider this possibility :)