Hmmm... Not quite!
Basic strategy is designed to tell you the best play given the composition of the entire deck or shoe. That composition changes once the first card is dealt.
Basic strategy does take into account the composition changes resulting from removal of the player's cards, and the dealer's upcard. So if you're alone against the dealer (as TheDave speced), and basic conflicts with an index, you're slightly better off with basic.
Now, unless you know a composition dependant basic (some of us know a few 3-4 card plays), you may be able to improve expectation by using indices in place of total dependant basic after the first hit. But on the first two cards, basic rules.
If there are others at the table, it likewise may be possible to improve expectation on your first hand by using indices instead of basic.
All this confusion could be avoided if counters learned "zero count" strategy instead of the optimal basic strategy. But since no count system has a PE = 1, this would also entail some slight inaccuries.
ETF