Not quite yet, orbital missions are much higher energy than lobbing something to space.
Specific energy of New Shepard booster at apogee: ~1000 KJ/kg
Specific energy of Falcon 9 booster at MECO: 2500 - 3400 KJ/kg
Yeah, and Falcon 9 is several times the size of New Shepard. There are several nice graphics here that explain the differences between Falcon 9 and New Shepard: http://space.stackexchange.com/a/13188