Besides the height of the card, the connector that fits on the expansion port of the motherboard will shift the accelerator card a few cm to the right, so it probably won't fit in the case any more.
This project would leave everything exposed and wouldn't be physically stable, which will only lead to system instabilities. If you want to expand with a PCI bus then you should at least consider getting a PC tower and converting it.
The D-Box tower is expensive, but it's worth it.
--
moto