Like UnknownSoldier says, take it to BMW and get the original sale info - that'll tell you if the engine was included.
"The car has lowered suspention, (can hardly fit fingers in wheel arches)
A full ac schnitzer body kit,
ac schnitzer wheels
ac schnitzer exaust system
and the interior trim is all ac schnitzer, It has Dark black wood trim with the ac schnitzer logo.
The car is done very tastefully, aparently the upgrade on the standard e46 was in the region of £15,000 to £20,000 over the standard price."
Bodykit, wheels, exhaust, and interior - that could easily be all the 15k used up. Schnitzer stuff is nice, but because of the cost - you mostly only see cosmetic Schnitzer mods. If it had the engine too, it would have probably got a Schnitzer model number instead of the standard BMW one - I doubt the original buyer would have paid for a 323 to get it modded this way.