Yes, many times there have been people in line for succession who were constitutionally ineligible. They would be skipped. I suppose that understanding could be challenged.
Elaine Chao, a Secretary of Transportation, would be 13th or 14th in line—but barring a Constitutional amendment, she could have never become President, because she is a naturalized citizen, not a citizen by birth.
The highest-ranking official who was disqualified for the Presidential succession was Henry Kissinger, who as Secretary of State under Nixon would have been fourth in line if he hadn’t been disqualified by being a naturalized citizen born in Germany. (Actually, between October and December 1973, Kissinger would have been third, since the office of VP was vacant.) If some catastrophe in mid-1973 had taken out Nixon, VP Agnew, House Speaker Carl Albert, and Senate President pro tempore James Eastland. . . then Kissinger would have been skipped, and Treasury Secretary George Shultz would have taken over as President. It is perhaps just as well that that didn’t happen..
Madeline Albright, who was born in Czechoslovakia slso was Secretary of State, in the Clinton administration.