Is a road bike worth getting for the "recreational rider"? How much do I need to ride it to make it worth it?
Absolutely. If a hybrid is a toyota camry then a good road bike is a porsche 911. Night and day difference all around
How much faster and efficient is a road bike over a hybrid bicycle?
Depends on the hybrid, but a road bike will be measurably faster since it is more comfortable and you are in a more aerodynamic and powerful riding position.
What brand/type of road bike should I get? I'm working with no bills to pay, so I'm looking to spend in the 1000-1700 range.
You can get something really nice in your price range, a week or two ago REI was clearing out the caad10 with ultegra for $1600 (normally $2k), that would be on the top of my list for a new bike however you need to include things like bibs, probably a saddle, clipless pedals, shoes, etc... so it might put you over budget, and you don't really need that much bike to start off with anyhow. There are lots of good options, use the search function and good luck.