Full fairings for upright bikes were made for the IHPVA races, back when people still thought that upright bikes were competitive in that event. Look around on recumbents.com or the IHPVA site for pictures.
There is still some people that do it, for folding bicycles. AFAIK there is no separate timing event for folding bikes, it's just another flavor of kooky people.

Also do note: a front fairing & body sock is a lot more practical in day-to-day use, as I have read it.
1--It has some 'give' to provide better sidewind tolerance (rather important for a upright bike),
2--it is VERY lightweight compared to any full hard-shell fairing, and finally,,,,
3--it is cheap. It is easily the cheapest of all. And it can be REALLY cheap if you construct the front fairing yourself by stretching fabric over a thin tube frame, and don't use one of the fancy blown-polycarbonate fairings.
4--it still drastically cuts your aero drag. Not as much as an ideally-shaped hard shell, but still way betterthan nothing.