Yes, they built over 11,000 between 1937 and 1945, about one third of the total Bf 109 production. The biggest "series" was 8,298 units.
And they produced Arado Ar 65, Heinkel He 51 and Gotha Go 145 under license before Bf 109.
So all is fine, one learns something every day.
EDIT: I believe you. My source was
Dr. Robert Kluge Freier Journalist Luftfahrt