Do the breakable wooden crates contain supplies?

Solution 1:

James Kane, one of the developers of Black Mesa Source has been quoted saying the following;

We already have a crate which is unique to all others which gives supplies, but are very limited in locations. However, standard crates in all the variants may contain goodies, junk, or air. It is our decision to keep it as such for rewarding players who like to explore, examine, and break random crap.

A special undisclosed crate will give supplies but standard crates may contain either goodies, junk, or air (type regardless)

^{Black Mesa: Source Props & Textures}

Solution 2:

In the Steam version of Black Mesa, the small H.E.V. crates with the Black Mesa logo will always have supplies. The label on top will show what type of supplies are inside.