Can Liquid Plumber come up into the toilet from the shower drain?

A few weeks ago we used Liquid Plumber in the shower drain. Then the cat started getting sick and we didn't really put two and two together until I noticed the cat drinking out of the toilet a couple days ago. Then I remembered that we'd used Liquid Plumber in the shower... could it have come up through the drain and into the toilet somehow? We'd taken our cat to the vet's a couple weeks ago but they couldn't find anything wrong with her. I'm just curious if anyone is familiar with pipes and how it works.