The object limit is 2559 in MP (note that level settings won't change it, so you must test it in MP in order to get the increased object limit). Barrels and crates take up only one object from the array and the extra objects are allocated when they are destroyed (they store what they must spawn and how many of them in their object data). The generator still takes up another object as normal, though.

Also, the unloading trick won't work in MP.