No, when they read a scan, they're supposed to read everything visible for every problem. Think of it this way: if you break your leg and they take an MRI, do you want the radiologist to miss a tumor because he was focused on the break?
To my knowledge, studies have not shown any benefits of regular full body MRI's. You might find a problem, or you might find a non-problem and in the process of fixing it (aka operation / medication) you create a problem. Those two effects seem to balance out each other on average.
I suppose a full body MRI would be very expensive and take a lot of time to read.