A creative idea, but there would be some complications.
The eMac has a U-shaped logic board that is double sided. CD/DVD drive and RAM/battery on the bottom, Processor and Hard Drive on the top, and USB/IO ports/Power button on the side. It is secured to a steel bracket that can't be detached easily. That means that even if it fit sideways, USB ports would be inside of the case itself with the CD/DVD drive, the power button cannot be pressed without opening the case, and the CD/DVD drive wouldn't be able to be accessed at all.
Furthermore, the power inlet and fan are separate components, meaning that they are not connected to the Logic board as you would think they are. The inlet accepts and deliveres raw power, so it doesn't have a transformer on it, instead, it sends the power to the CRT board and then back to the Logic board from the CRT board. So, without the CRT board, you get no logic board power.
So, yeah. That's why it would be very very VERY hard to accomplish this.