No, it couldn't be. It would have to donate an electron pair to be a Lewis base, or accept a proton to be a Bronsted base. It cannot do either.
A Lewis base must be able to donate an electron pair...
"BH"_3 contains 3 + 3xx1 = 6 valence electrons: 2 per single bond.
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Therefore, "BH"_3 is a trigonal planar molecule, which only has three electron groups. Of course, "3 electron groups" - "3 bonds" = 0, so it has no electron groups remaining that aren't bonded.
Furthermore, despite having a spare 2p_z orbital, it's empty---it contains no electrons:
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So, "BH"_3 cannot be a Lewis base.
A Bronsted base must be able to accept a proton, i.e. an "H"^(+), like this:
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An "H"^(+) has no electrons to donate, so this is done by having the so-called Lewis base donate an electron pair, which is not possible for "BH"_3 to do...
Hence, it is not a Bronsted base either.
