Can i trade in a reconstructed title? NEED HLP FAST?

Ok so tomorrow im going car shopping i found a 05 350z for 15k and i was wondering if the car dealership would take my car its a 2000 gt eclipse with 85k miles aftermarket rim/wheels/intake/header/cat back/and paint job excellent shape except for the fact that its a reconstructed title i still owe about 2k on the car and was wondering if you guys think theyll take the car or atleast pay it off for me so i can buy the car.