One day you may walk in and they'll tell you to leave it outside. The next day a different manager may be perfectly fine with it. Nobody here can tell you what will happen.

And especially if you're utility cycling, the "My bike is cleaner than X" argument really doesn't fly, especially the first time you're maneuvering through a crowded aisle and someone brushes up against your chain.

As other people said, buy a cheap utility bike and use that for shopping and bopping around town.