More or less: yes. It's the combination of both removing those excess bytes.

If you transmit 10 static files per page request, and have 256bytes of cookies you're sending 2560 bytes of cookies, or 2KiB per page load. That's on the end user's upload bandwidth too, which is typically dramatically less than their download.

The lessening of the connection limit also allows more entities to load at the same time, the combined effect is a good increase in speed. Two tweaks for the price of 1. =)