Is it feasible? God no. And IMHO not worthwhile either - you're taking a light FWD car and adding a few hundred kilos for AWD. If anything RWD would be a middle of the road option, but honestly, converting any car from its original drivetrain is pointless as far as I'm concerned, if you want AWD, go buy a WRX.
Is it legal? Unlikely, but I'm not positive. Maybe if you slipped enough folding stuff to the engineer...
i have news for you my friend as it has been done before! you will need the entire CRV drivetrain and convert it over to your CRX. bear in mind that the CRV transmission is notorious for being weak....and when i say weak, i mean any sorts of power upgrades and it will go BANG!! therefore you will need to upgrade it, especially so the drive shafts and differentials (rear are tiny) To fit the CRV tranny into the CRX you will need to HEAVILY modify the CRX floorplan, which will be another huge pain in the arse.....and this will cost shit loads..that is if u have any money left-over from the purchase of the crv drivetrain, not to mention the amounts of hours require for labour for fitting. It's actually easier, not to mention cheaper to have 2 engines, one engine running the rear wheels, and the other running the front wheels. what is an even better idea is to convert your CRX in a RWD! it has been done numerous times and will not be as much of a headache compared to the 4WD. Many people have considered 4WD conversions for Honda, but most are put-off when they realise how difficult and expensive such a project is......and also if u have to have deep pockets, with alot of time, with the intensions of going rallying with it, if not i wouldn't bother mate!
If i have not yet put you off the idea.....then here is some pictures of a 4WD CRX with a B18C engine and CRV transmission.....
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