Using a new chain on worn out sprocket?
If your chain was measured and is worn, then by all means replace it.  You are going to cause more wear to your bike using a worn chain than having slightly worn sprockets.  A worn chain causes uneven wear on the teeth of your chainrings and cassette cogs, eventually this can cause issues with shifting and 'chain suck'.

The new chain you selected looks good. Before you install it, please clean off any grease and grime from your front chainrings and cassettes.  It should be good without re-lubing for a couple hundred miles with the factory lube, after that you should make sure that you keep it clean and lubed regularly.  

The life of your chain is proportional to how you maintain it, a good chain poorly maintained will last a couple thousand, well maintained I don't doubt it could last 10k.

More info on chains: http://sheldonbrown.com/chains.html