I'm willing to suspend disbelief regarding the issue of the pets for the sake of appreciating the point the writers were trying to get across. The scene with Michonne amid the walker herd was, on the whole, powerfully effective, particularly after she saw her walker doppelganger, which jolted her out of her desire to walk with death. It reminded me somewhat of a scene from the movie Midnight Express, where Billy, the protagonist, is shown at one point "walking the circle" with the other insane prisoners, symbolizing his final descent into hopeless madness. When Billy receives a visit from his girlfriend, he's similarly jolted from his catatonic funk and he begins to want to live again.
What he said.
It really doesn't make sense that just by tying up 2 walkers would make you invisible for the others but I can let it pass since it is used to show the state Michonne is in. She decided it was the best to be on her own and going back to what she was before she met Andrea and the group, then realizing that she would rather risk it with the living than be safe with the dead, which ends up in slicing heads.
If it was used in a way of "Oh yeah, look how cool I am with these walkers on the leash, I'm such a badass." which I know some showrunners would probably do (yes Mazzara, I'm looking at you) it would be more of a problem.