Yup. As far as I know we always had the TOS VHS tapes (the ones that came in the grey/silver old-style cases, with two or three episodes each - and I'm led to believe they were horribly expensive!) and the movies. TNG started not long after I was born, but from the time I could operate a VCR (basically as soon as I could reach it) I was watching TOS.
Funny story - we never had/lost the tape with "Turnabout Intruder" on it, and while I have watched every TOS tape we had multiple times - I spent many a summer morning waking up before everyone else so I could have the TV first and watch Trek - I have never seen that episode (or whatever other episode was with it on the tape).