For smithing and tailoring, the answer is probably no. It can depend on what exact prize you want I suppose, but in general, I'd say no.
For instance, I just looked into the following LBOD:
15 exceptional Ringmail, copper ingots.
This gives 725 points still (25 for 15 count, 200 for exceptional, 300 for copper, 200 for being a ring LBoD), or 145 if banked.
Now, each individual component would give 525 points (25 for 15 count, 200 for exceptional, 300 for copper). That means each component would bank 105 points.
So... you can either turn it in as an LBoD for 725, or you bank all 4 of the smalls for 420 points.
BUT WAIT... What if you bank 3 of them for 315, and then turn in the 4th now for 525, so you get 840.
This seems a bit broken - turning in the components of an LBOD individually shouldn't be possible to get a reward than if you turned in the LBOD filled.
For instance, I just looked into the following LBOD:
15 exceptional Ringmail, copper ingots.
This gives 725 points still (25 for 15 count, 200 for exceptional, 300 for copper, 200 for being a ring LBoD), or 145 if banked.
Now, each individual component would give 525 points (25 for 15 count, 200 for exceptional, 300 for copper). That means each component would bank 105 points.
So... you can either turn it in as an LBoD for 725, or you bank all 4 of the smalls for 420 points.
BUT WAIT... What if you bank 3 of them for 315, and then turn in the 4th now for 525, so you get 840.
This seems a bit broken - turning in the components of an LBOD individually shouldn't be possible to get a reward than if you turned in the LBOD filled.