Wouldn't recommend it.
You might save one HTTP request initially (remember a CSS -file- is cached), but in the long run clicking around I think you'll find the gain is minimal if any, AND you're adding extra text to be sent through with every request. Maintenance is important to consider too.
Depending on the amount of CSS/frequency of page laods on mobile versus ajax loaded data you might be able to sneak in some load time savings if you include the CSS inline, but that's a case by case judgement - the safe answer is to put it in one file that is cached automatically by the browser.
Check out the size of the HTML on that page, more than half of it is CSS.