Yes -- the dakuten and handakuten marks are very systematic modifiers of the readings of the underlying glyphs. The dakuten more or less voices the leading syllable (ka -> ga, ta -> da), and the handakuten only applies to H*-column kana and changes the sound to a P*. From my perspective, you only really need to learn the base kana and remember the rule for the modifying marks -- you're not learning entire new kana after that.

(There's also combinations like kyu = ki + small-yu, but that also just builds on the kana you already know, and behaves pretty logically.)