Not really. It's more complicated. カリ活用 is applied only to specific auxiliary verbs such like ず, き for the past tense or しむ for causative. So, for instance, the adverbial form (連用形) 少なく, not 少なかり, is used to continue clauses even in classical Japanese.
e.g.
少年老い易く、学成り難し。
(易かり is not used in here.)
As for ず, the imperfective form (未然形) and the conclusive form (終止形) are also ず,and furthermore, ず has other 連用形 ざり and に.
e.g.
用法決して少なからず。(= 用法は決して少なくない。)
類似の質問少なからざりき。(= 類似の質問は少なくなかった。)
Thus, "から and く" or "ず and なく" are not the one-to-one corresponding between classical and modern Japanese.
Incidentally, there are other negative auxiliary verbs じ and まじ. Classical Japanese is complicated even for natives, indeed.