I wouldn't. I've left bicycles unlocked outside supermarkets when I've forgotten my lock - and my Fixie is never locked outside London.
I think it would clutter the aisles up.
But I admit (in shame) that I had one of my only recent "Pompous Git Moments" at a Tesco store. I still shudder when I recall it, even though I was technically 'in the right' at least in part.
The wholly inadequate cycle racks at our Tesco had been moved a few times and ended up out in the open beyond a big trolley park, not anywhere near the route from entrance to doors.
They were impossible to see and there were no signs...
So... I locked my bicycle up against a pillar, not in anyone's way. Out came (to my surprise) an Assistant Manager who asked me to move it to the bicycle racks. I was almost in the store by then and had picked up a basket, so I asked why. It was an H&S issue and I had to use the racks provided. I was perplexed and got that little twitch that warned of an impending muted snobbo-rant.
I got all Home Counties and asked the bossyboots to see how many of the cars in Child & Toddler contained children and toddlers - also how many cars in the disabled bay were displaying stickers. In both cases the answer is usually none or very few.
I think I was quite offensively snobbish in my attitude and tone. She backed down and went back to the Customer Services area. I did my shopping.
I still wonder why on Earth she chose to tackle a cyclist locking his bicycle where nobody could possibly trip over it or have to divert to get round it... I still question why that was worthy of intervention when the regular missuse of Child & Toddler and Disabled Bays is far more of an issue.
But... I still wince when I think of the sneering, snobbish, entitled and condescending tone I took.
I still shop at Tesco, but would not take my bicycle or my car into a store.