No! The accumulator must remain upright! What you can't see in the otherwise excellent drawings posted by
ltlfrari is that there is a small hole in the bottom of the U-shaped outlet tube of an accumulator.
The primary purpose of an accumulator is to trap any liquid refrigerant that makes it through the evaporator, ensuring that only vapor is supplied to the compressor. As you can see, the U-shaped tube takes vapor from the very top of the accumulator ... but that leaves no way for refrigerant oil to get out of the accumulator to the compressor, and the compressor requires a constant supply of lubricant. That's where the small hole at the very bottom of the U-shaped tube comes in ... it bleeds refrigerant oil into the vapor returning to the compressor.
Edit: Added a more detailed schematic drawing of a typical accumulator (from Automotive Heating & Air Conditioning, by Mark Schnubel).

For what it's worth, no Fiero uses a receiver-drier ... which operates on an entirely different principle than an accumulator. An
accumulator is always installed between the evaporator and the compressor, in the low-pressure/vapor section of the A/C loop, while a
receiver-drier is always installed downstream of the condensor, in the high-pressure/liquid section of the loop.
[This message has been edited by Marvin McInnis (edited 05-23-2007).]