This is one of the greatest questions.
We can be sure that people will surrender their liberty as they have many times in the past, when it appears security and comfort can be gained.
But every...
yes, on space shuttle, space station, Apollo, Saturn and Mercury missions, Soyuz and Mir, artificial satellites and orbitors. LOTS of computers up there.
With today's technology, Humans have more insight than computers and life appears to be more vivid than the computer's. But that may change someday (It will).