If I plug in iPod to my computer, can the Nautilus access the storage?
If not, then what would be the best application to access an iPad/iPod (apart from Banshee)?
Yes, you can access ipods from nautilus. But all files that you synchronise to an ipod are renamed and stored in folders, that are managed by an ipod-database. So it doesn't make sense to use nautilus.
The best application depends on your apple-device and software version. After all my attempts with different iPods, I found Banshee to be the most reliable
If Banshee doesn't work for you, try Gtkpod, Rhythmbox, Amarok and Songbird. Sometimes they worked with some iPods, sometimes not.
If nothing else worked, I used iTunes in a virtual box running Windows XP.
Rhythmbox works absolutely fine for iPods other than Touch/iPhone and will be able to do anything you want it to, like transferring songs from computer to device, deleting songs and even transferring songs from device to computer (which iTunes cannot do). In fact, it syncs much faster than iTunes, though editing tags is hard (you need to edit the tag on the song in the Library, then delete the one on the iPod and transfer from Library to Device).