This is correct. Harlan Ellison was assigned his story for STAR TREK back in March of 1966, That would be in the range of a month or two of THE TIME TUNNEL's pilot being completed, so there would have been no chance for Ellison to have sampled the Allen series beforehand.
Knowing how frugal Irwin Allen was, he wouldn't have paid a known writer to write for his shows - not at that point anyway. He did seek out a few in the early days of VOYAGE TO THE BOTTOM OF THE SEA, but then cheaped out on that show too.
THE TIME TUNNEL didn't usually delve into any deeply personal territory with its shows, sticking rather with the fistfights and joining in with whatever the crisis of that time period put them into. There was one story late in the series run where James Darren's character falls in love with a woman back in the Marco Polo episode. He wanted to remain rather than be transferred out but later saw the error of his ways. It didn't have near the emotional impact of the "City On The Edge Of Forever."
A while back, I think I spotted it here on this forum, someone brilliantly made a mash-up photo of COTEOF and TIME TUNNEL:
I'd love to credit whoever it was, but sadly don't have the information - but it IS BRILLIANT!