Firstly unless they agree to sell it you, you cant just take stuff off it they own it if they are paying off your claim and you would be stealing parts off their car.
Secondly the thing you would think is the best item to have i.e the engine you will likely find takes months and months to sell and even then you wont get much for it, or at least that's my experience.
to make a reasonable amount from it you will have to be prepared to do a lot of work, have storage for a lot of parts, be prepared to post dozens and dozens of parts at small value and you'll still likely have some of it left in a year or more.
If any of the above doesn't sound like fun, don't bother.