Not as far as I know. Maybe the spiders to too hard to train or work with?
Also, giant spiders are descended from Ungoliant, who rose up against Morgoth. I doubt Morgoth or Sauron had any love for these creatures.
Besides, they seem more suited for terrorizing smaller bands of characters, freeing up the Orcs for military matters.
I doubt Morgoth or Sauron had any love period, but I get your point.
"Sauron In Love" sounds like a really bad fanfic!