Hi Maty,
As long as it is not turned on, I don't think you will have an issue. Be sure to eject any disks in the optical drive before powering down.
However, there is another action you can take that will help the school. Removing the "PRAM" battery before storing will help avoid problems when the school sets it up this fall. Here are Apple's instructions for accessing the battery:
eMac: How to Replace the Backup Battery
If the battery has never been replaced, I'd toss it and buy a new one. Such batteries are seldom working after 3-5 years anyway. However, don't install the new one until you actual deliver the computer to the school--that way the battery will be at full power. Tape the new one to the outside of the case or the box so it doesn't get lost. I buy those batteries online here:
http://eshop.macsales.com/item/NewerTech/BAA36VPRAM/
If you opt for the US Postal Service delivery option, I think OWC won't charge shipping. Even if they do charge, it is still cheaper than buying from the only retail source I know--Radio Shack. RS have the same battery as part number 23-026 but charge over US$15 for it and you have to drive to the store.
Hope this helps,
Allan
eMac USB 2.0 2005 1.42 gHz; 2GB RAM; Mac OS 10.5.8
eMac 2002 700mHz; 768MB RAM; mac OS 10.4.11