Question, Hex, why did Gus want an eye on Saul? Walt wasn't on Gus' radar at first. Also what sense would it make it have Gus in the series if he doesn't interact with Saul? It would be weird to have a whole side story that had nothing to do with Saul.
These are very good questions with no real concrete answers.
Saul was a shady character before we ever seen him. The very first episode we see him, when Walt and Jesse have him in the desert, he mistakes them for killers and says in Spanish

"I'm forever a friend of the cartel!". Directly after that he suggests they kill Badger, who is going to snitch.
So the guy was tied into killers and gangsters before he ever met Walt. Someone like that Gus would definitely have an interest in just off GP.
And this wouldn't be the first time these writers developed multiple tangentially related story lines. The entire cartel story line in season 4 had no direct connection to Walt, neither did the flash back with Gus. Gus, and by extension Mike, could shadow Saul in the series.
Fred.