With modern GPUs from AMD and Nvidia both supporting some form of hardware-based video capture, basic video capture should work fine as long as your streaming software supports Nvidia's shadowplay or whatever AMD's equivalent is called.
A capture card is mainly necessary when you want to use a separate PC for recording/streaming to eliminate any chance that streaming may interfere with the main PC's performance or when the main PC simply doesn't support a satisfactory form of local recording, such as recording BIOS or OS installs where there is no working OS on the computer to record from.