Yes, BASE is a Scrabble word!

Letter values in Scrabble US: B 3, A 1, S 1, E 1.

Is it a valid word?

BASE is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

installation from which a military force initiates operations
lowest support of a structure
a place that the runner must touch before scoring
the bottom or lowest part
(anatomy) the part of an organ nearest its point of attachment
a lower limit
the fundamental assumptions from which something is begun or developed or calculated or explained
a support or foundation
a phosphoric ester of a nucleoside; the basic structural unit of nucleic acids (DNA or RNA)
any of various water-soluble compounds capable of turning litmus blue and reacting with an acid to form a salt and water
the bottom side of a geometric figure from which the altitude can be constructed
the most important or necessary part of something
(numeration system) the positive integer that is equivalent to one in the next higher counting place
the place where you are stationed and from which missions start and end
a terrorist network intensely opposed to the United States that dispenses money and logistical support and training to a wide variety of radical Islamic terrorist groups; has cells in more than 50 countries
(linguistics) the form of a word after all affixes are removed
the stock of basic facilities and capital equipment needed for the functioning of a country or area
the principal ingredient of a mixture
a flat bottom on which something is intended to sit
(electronics) the part of a transistor that separates the emitter from the collector

Also: base of operations, al-qaeda, al-qa'ida, al-qaida, root word, free-base.

Not playable in Scrabble US: UNDERSTRUCTURE, QAEDA, MEANSPIRITED.