If you are very careful and do it in a dust free environment you might be able to get it to work enough to get the data off. You'll need to use the same model drive to swap parts with in order to do it though, and unless it is crucial you get the data, its not going to be worth the hassle since you will likely destroy two drives in the process.
Its usually easier to change the board out, which may be the defect part anyway, rarely does the motor itself die.
I do this sort of thing quite often and have a good bit of success, usually works long enough to get most of the data off the drive, which is good for the client and very good for my wallet