To back up everyone else, absolutely you can drive the car. No cars had (properly functioning) ABS systems until they miniaturized computers sufficiently in the 80's (a lot of those early systems are still pretty trash) and they weren't standard on most cars until the late 90's-early 2000's (when the tech matured & became cheaper).
No idea the OP or other readers car backgrounds so my advice will be given as it would to someone who knows nothing (not an insult, just trying to be more helpful to people who actually know nothing about this system).
You obviously can't individually apply brakes or pulsate them 10's, 100's, or 1000's, of times in a panic braking situation but usually not necessary (ABS is really only there for panic braking & allows you to continue steering & prevents a loss of control on slick surfaces or at the limits of the vehicle's grip) & the X's chassis & braking system are decent & designed to work without it.
Drive normally & release/re-engage as necessary (pump) if the brakes lock up.
You also won't have stability control so keep that in mind.
To repair, make sure you properly solder (use rosin flux, appropriate solder [I use 60/40 tin/lead for auto work but do some research], heat shrink [suggest navy heat shrink], & good technique) the system using quality wire of the same gauge. No idea whether it is better to solder the connector or straight solder the wires but I would try the connector 1st & not add any more wire or joints than you have to (go to a junk yard & hack a connector off if you need to).
Resistance levels from this sensor are critical to proper function so if this doesn't work (it trips a code or doesn't function properly) figure out a solution & report back so the community is aware.
For your 4wd I am including a possible solution. If you try it & it works please let us know.
ABS 4wd hack CLICK HERE
Here is the best soldering video I've found.
CLICK HERE for to the point soldering.
To the OP, if you are already a soldering god rock on, otherwise, I would suggest getting some wire of the same gauge as your connectors & practice until you have beautiful joints. Doesn't take much! Also, don't forget to put the heat shrink on before soldering, almost as annoying as breaking a connector.
Best of luck. Happy New Years!