Nope, you cannot catch/obtain any of the Eeveelutions (or Eevee itself) in the original B/W by regular capture from the wild. However, Eevee and it's evolutions can be seen by battling the following trainers:
Source: Various Serebii 'Trainerdex' pages:
You cannot get eevee or its evolutions in black.You have to trade from someone or poketransfer from previous generations.
If you want to see eevee or its evolutions,these sources should help you indicating which trainer has those which should help you fill up the pokedex.
Hope this helps!