If my memory serves me correctly, yes. However, most schools/flying clubs will insist on checking you just to satisfy themselves and more importantly, the insurance company that you know where every thing is and you can fly it safely.
You will notice there's no such thing as "MEJ". Multi Engine Jet. There's no training that will cover all jet aircraft in a certain category. That's why you have type ratings.
Also, some piston aircraft have unusual or tricky handling characteristics and they will have a specific rating too. To fly it you'll need to complete a specific detailed course.