Does "a pretty egg box" always mean "a pretty box of eggs" rather than "a box of pretty eggs"?

More precisely, is "adjective adjunct-noun head-noun" always interpreted as "adjective (adjunct-noun head-noun)" rather than "(adjective adjunct-noun) head-noun"?

If so, can "a pretty egg box" be punctuated so as to mean "a box of pretty eggs"?

Another more semantic example: "steel screwdriver box".