It's possible I wouldn't have. I was introduced to Trek through TNG, so who knows? I suppose, even without spin-off series Star Trek would eventually get a movie reboot, and maybe that would motivate me to check out TOS.
Of course, how divergent things are we? Even without spin-offs are TOS re-runs still being shown daily around the world? If so, then there's a good chance as a sci-fi nerd I'd still check out the famous TV show of the 60s.