Should I get a road bike?
It's all about having the right tool for the job. Road and touring bikes are designed for long rides on roads. In contrast, mountain bikes are designed to go off road, and hybrids are designed mostly for casual riding. If you're doing 200 km per week, you're serious enough about cycling to notice a serious difference when you switch to a road bike.

I recently made a similar switch. I was riding a mountain bike, which I used for commuting, off-road trails, and road rides. I eventually found that I was only spending about 10% of my riding off-road. I considered switching to thin slick tires, but it was obvious to me that I also needed more hand placement options, a more aggressive riding position, a higher maximum gear, and lighter weight. In other words, I needed a road bike. When I sold my mountain bike and got a road bike, I instantly noticed a 2 to 5 kph speed improvement for the same effort.

Since you're considering switching from a cyclocross bike to a road bike, you should expect a less dramatic change, but if you feel like you're losing out from using the wrong tool for the job, you might as well try a road bike. You could at least rent one for a day and see how it feels. Alternatively, you could consider switching just the handlebars and tires on your current bike, since it sounds like you already have a light-weight frame.