You can pretty easily empirically test this and conclude that your impression is not true, at least for GNU grep. :-)

    $ time grep 'ZQZQZQZQZQ' OpenSubtitles2018.raw.en | wc -l
    0

    real    1.089
    user    0.230
    sys     0.858
    maxmem  5 MB
    faults  0

    $ time grep -E 'ZQZQZQZQZQ' OpenSubtitles2018.raw.en | wc -l
    0

    real    1.094
    user    0.210
    sys     0.883
    maxmem  5 MB
    faults  0

    $ time grep -F 'ZQZQZQZQZQ' OpenSubtitles2018.raw.en | wc -l
    0

    real    1.096
    user    0.223
    sys     0.872
    maxmem  5 MB
    faults  0