Hello, Chocdee,
Mounting a right-handed pickup the wrong way round might work if there's plenty of clearance inside the body routings. On the other hand, it might not.
Here's an illustration of standard pickup routing on a Strat:
http://www.bhefner.com/images/products/S.FLOYD.SWAMPASH.jpgYou can see that the cavities for each pickup are shaped to allow the pickup to be installed only one way (the correct way) round. Trying to install a pickup back to front (ie, with the solder contacts facing the neck) may not be possible - in fact, it's likely that it won't be, with a standard three-cavity routing.
But... some Stratocasters (perhaps including the American Standard model) have a single, large, routing which will allow the pickups to be mounted the wrong way round without problems; for example:
http://www.wilderdavoli.it/images/imgw/gbsap66.jpgSo check out under the scratchplate before taking that advice about turning the poickups around. Another way to do it might be to slip the magnets out of each pickup and re-insert them in the correct stagger for a LH guitar (it's usually possible to remove and replace the magnets, especially on a fairly new guitar).
Best wishes,
JN