No, but in a roundabout way, sorta. Boring is a bad way to increase power because you get such small increases in displacement. A 3.8 bored over would only be about 3.9L maximum.
You can stroke the engine, however. In fact, there is a kit to stroke a 3.8L to 4.6L. You also have to bore the engine to get this displacement. You can NOT use the 4.6L V8 pistons, though, because they are way too small.
The best option for a 3.8L is to look to the Ford 4.2L V6 available in trucks. They're the same engines, everything is interchangeable. The only difference is stroke. You can put the rotating assembly from a 4.2L engine in a 3.8L engine and make it a 4.2. If you're planning on doing this in a Mustang, however, you'd want to keep the Mustang's intake manifolds. The truck intakes will not fit under a Mustang hood.
For more info on hopping up a V6 Mustang, check out www.v6power.net. It can be done, but there are MUCH easier and cheaper ways of going about it than trying to build a radical 4.6L V6.