YES, but not due to "bad tuning". In the late 1700s, Pascal Taskin, the Paris Court tuner, used an A tuning fork that sounded 409 Hz (between G and G#). The modern standard for A is 440 Hz. Michael Praetorius wrote in the early 1600s that the orchestra in Gröningen, Germany, tuned to at least 523 Hz or the equivalent of a modern C-natural (and possibly higher).
Clarissa said, "Bach was possibly using a tuning system based around A=150 Hz (but of course we can't know that for sure)", but that is surely incorrect. First, 150 Hz is almost a half-octave from an A, midway between D and D#. Second and possibly more important, tuning forks were in use at the time, and Handel (a German contemporary of Bach) owned a tuning fork that has been preserved, which is pitched at 422.5. The tuning fork of Franz von Weber, an earlier German, is 424.1 Hz. They differ by only 0.4% and are midway between our modern G# and A.