to add to mpilch's answer:
nowadays onboard components use mainly software mode emulation for their functionalities - which translates into some CPU load, as high as 30% CPU load on a single core 2 GHz system - if you happen to play an online game with 5.1 EAX 2.0 sound (like Realtek ALC8x0 codecs allow you).
This translates into more or less 7% on the ethernet side, the rest on sound.
Now, if you have a dual core CPU, said load gets almost irrelevant. Considering that most add-in network cards do the Ethernet translation in software anyway, getting a card that does hardware ethernet encoding, routing and IP translation costs more than the CPU and mobo combined. A card that does hardware-based EAX 2.0 (or more) costs less, and will yeld much better results. On the other hand, if you merely play stereo games, onboard solutions will yeld slightly better results due to less electrical interference - provided you have a good quality mobo with a well-set DAC (ASUS boards have good onboard sound quality, for example)
Short answer: yes, onboard solutions weight on the CPU. No, if you're not into very high quality accelerated games sound or into high-speed server business, you don't need add-in cards.