Can these composite warships take a hit/endure much damage?
There have been some interesting discussions about the survivability of these ships, but the composite materials aren't the primary concern.
The concern lies with the Tumblehome hul design. Keep in mind, that the Tumblehome design is not new (as mentioned, earlier, it dates back to the American Civil War), and while it has some advantages - even in a pre-radar environment, where it offers the same benefits for shell deflection as sloped armor does on a tank - it wasn't pursued to any great extent in the 20th century for a couple reasons.
Tumblehome ships have greater tendency to "nose in and down" into waves in heavy seas than a traditional hull design that flares outward above the waterline. There has been a lot of work to mitigate the safety issues associated with this in the Zumwalt - basically a much more sealed upper deck, which won't prevent the behaviour, just reduce the water ingress and risks when it happens.
The other concern is about the size of the internal air pocket above the waterline if the ship receives a below the waterline hit. With a traditional hull design, the size of the air space increases the higher you go in the hull. If a ship starts taking on water, this creates air pressure and buoyancy conditions that, while it may not save the ship, will keep it afloat for longer. Possibly long enough for successful damage control, but also creating a longer window of opportunity for crew evacuation.
With a Tumblehome hull, the largest internal air pocket is below the waterline, which creates some interesting problems with a below the waterline hit. This is actually the key reason the design was dropped from warships at the beginning of the 20th century.
The Navy's answers to both these concerns is, essentially, "trust us, we've solved this, with some cool technology we don't want to discuss." Not everyone is convinced.
http://www.defenseindustrydaily.com/defense-news-will-ddg1000-destroyers-be-unstable-03203/
The other thing to consider is the nature of modern anti ship missiles and torpedoes. They have become powerful enough to cut any modern destroyer in have, with very low survivability prospects. Part of Navy is pushing for a larger fleet of smaller vessels with less crew per vessel, to increase overall survivability as a result. The Zumwalt fits within those parameters.