X10 = theoretical 256 maximum variations.
These are not good odds for security.
This kind of locking arrangement will likely negate any household insurance you carry against theft from your property.
There are actually 4 hands of doors - Left Hand, Right Hand, Left Hand Reverse and Right Hand Reverse. Any hand of door can be controlled with some kind of access control mechanism, so can Dutch doors, barn doors and overhead doors. Point is, the handing of a door does not make it more or less difficult to control.
You could probably squeeze that electric strike from the link into your door frame and get it to release your door remotely but
a) it's too deep for a standard residential (or commercial) door frame so you'd have to cut out some studwork to make room for it (removed studwork = weakened structure), and
b) A standard residential entry lock has a feature which (when the lock is installed correctly) prevents the latch from being opened easily via the slip (or credit card) method. This electric strike will stop that feature from working correctly and the door will be very easy to slip open with no signs of forced entry.
Any form of access control should be considered a convenience feature and not a security device. You're getting closer to reasonable security of your X10 code if you do what Brian mentions with the doubled up modules, but that still won't protect against slipped entry methods, nor will it magically make your insurance company pay out when your 100" plasma TV is stolen with no signs of forced entry.
BTW, I know credit cards don't work very well for slip attack unless you're making a movie, but there are items out there that are much more common and much more effective
If you're not worried about home invasion, theft, burglary, or weakening of the structure then what you've picked out will work just fine