gdgt

Simple answer. No.

Complicated answer:
This is impossible with the iPod 2nd gen you've tagged. This iPod is only able to sync while connected to a computer. So, you could sync it, then leave it in the room, but any updates to the iTunes library won't show up until the iPod synced.

The only iPod that could sync to an iTunes library is an iPod Touch 3rd or 4th Generation, with iOS5 installed. iOS5 allows for wireless syncing over WiFi, but is limited to the size of the iPod.

Your best bet would be to look into an Airport Express, or an AirPlay compatible Receiver/Stereo. These will allow you to stream the music from your computer directly to the sound system. With this you can control it with your iPad using the Remote App.

I have AirPlay on my Pioneer VSX-51, and it's absolutely great, it's a great party trick to play the music from your phone. A very nerdy party trick...

As ajcohen pointed out, the iPod 2nd-gen isn't capable of wireless syncing. However, you asked about iOS devices. iOS devices can now take advantage of iCloud to store their entire music library. With iTunes Match, apple will legitimize your entire library, even replace lesser quality tracks with their higher quality versions. A one time fee of about $25 gets you a complete music collection, stored in the could and instantly downloadable to any iOS device or mac, on wifi or 3G. And, if your like me, who has different songs on different computers, this will unify your library of music across all devices.

How this effects you in "everyday life" is this: if you were to rely on the wifi sync method (with iTunes) you would have to choose to update each time to see new songs added after its last sync and the phone does an entire sync, not just a quick sweep of new music, so this takes several minutes or longer depending on your connection. You then have to locate the new songs (not a big deal if your importing a couple tracks, but progressively worse if your importing large groups of music, say ripping all your old mix tapes.) there isn't a newly added list.

Using iCloud, your entire library shows up on each device with tracks that aren't on the device but are in the cloud shown with a cloud symbol next to them, which when pressed, will download the song immediately. You can also choose to import entire albums at a time. It's a much more elegant way to share your music with all your devices and its best feature is that it doesn't matter if you're at home or on vacation in tahiti, all your music, every track, is right there waiting for you.