this is an old argument, the "tune like the dropped guitar player" vs. "play a regular 5-string" people.
for most metal guys, matching the guitar tunings just makes more sense. (this is also why 5 and 6 string basses can be weird for those styles, it's harder to get them into the same tunings as the guitar players, who are often somewhere below E but above B.)
anyway, you aren't gonna hurt anything, as long as the neck is still adjusted to be nice and straight. it might feel a little unbalanced though, with the B feeling more limp than the other strings.
you could get a super-light 5-string set, then swap in a regular-sized B, so the tension evened out more.
Guitar Repair Gnome
Alpha Music, VA Beach