Yes, you can see the SD-card of emulator.
Go to DDMS -> Click on Filer Explorer -> Mnt ->SD-card where you can see all your file.
If you don't find Sd-card inside DDMS then might be you have not allocated space for SD-card if it is so then add it like this
After allocating space you will be able to use that space as SD-card.
Does that space allocated for the SD card be automatically unallocated after I delete the AVD?
Yes when you delete AVD it will automatically delete all the file which you have created and un-allocate space.