You can. But I've put about 30 albums on my phone and I have little internal space, so I just put a "small list" on it.
But for what it is worth 1 GB may be fine. Handling 30 albums would be a nightmare with the Shuffle.
It works (as the name says) if you want to listen to a playlist in shuffle. But for me (and my ex) it didn't work for anything else. So we both found out we didn't had any use for this device.
The later model had 2 GB and had playlist functionality. I had both the 1GB 'continuous playlist' model, loved it it was perfect for mix-tapes, it also loaded albums with the songs in order, so yes there was a lot of skipping to get past an album, but not a problem. The 2GB model if you held down the "f-key" on the top read out the names of playlists ,ie albums, and let you press skip to cycle through them.