I'm not an expert by any means. But, I did a bit a research on this.
First off, as pursuant to the other person who mentioned OAK, this is not an OAK per say. An OAK is usually referred to as outside air for combustion. THis is a CAK, a Chimney air kit. It draws air from the outside and runs up the inside cavity between the two walls of the SL300 pipe and out the bottom holes on the termination cap up top.
IMO, the design is really more economical, than purposeful. It works to keep the outside layer of the pipe cool enough during a chimney fire as UL tests dictate (so many degrees for X period of time), and any combustibles within 2", from catching fire. They use it, because it's the cheapest. Alot of people looking to install a fireplace, would opt out if the cost included another $1200+ of triple wall stainless insulated chimney. Also, to certify other chimneys, costs money. Personally, I do not like the SL300, or any double wall air cooled, it just is prone to too many issues. As you mention, if running cool outside air (the colder it is outside, the more persistent the issue) on a hot pipe, yes depending on conditions, it might be prone to condensation. That said, if you read the install instructions carefully, they always make sure to tell you to insulate any chase, whether the chase is inside the home, or on an outside wall, so the air inside the chase will become balanced quickly and not prone to outside 70degree, or 10 degree air. With those conditions, it should not develop condensation, or so they say. The other complaint is, it might develop more creosote, because your running outside air up the pipe to cool it. For anti-cresote conditions, it'd be best to keep that pipe as hot as possible.
That said, the pipe acts differently depending on conditions, every install and every temperature might be different. The best thing to do is, watch it carefully at different outside temperatures and see how it acts. It might develop condensation, it might not. And you should always inspect a new install every few weeks the first year to see how creosote, if any, is progressing, to learn how your chimney and install work together and how creosote develops in your particular conditions. If installed according to specs, it shouldn't, but I've heard of complaints of condensation. I have the SL300 on my North Star fireplace, it's installed 28' of it in an insulated chase, the chase on an outside wall. It does not develop condensation that I've noticed.