No. All buildings are required by law to have staircases big enough to evacuate all the building occupants within a few minutes in case of emergency. StepJockey will increase stair use in your building significantly, but it will not fill them to capacity or anything near it.
And that in itself has benefits. Rather than being empty, slightly stark places, your building's stairs will quickly become well-used and populated. We'd be pushing it to say that they will become a party destination, but you get the idea. A little bit of human habitation goes a long way to making even the barest of stairs warm and welcoming.
StepJockey Smart Signs won't cause jams. Tapping or scanning the signs only takes a moment and we always place smart signs outside the entrance to the stairs (to nudge people in) as well as inside to make sure people have options.
If you want to warm up your stairs further, consider using some of our funky stair graphics to brighten them up a bit. They are low cost, easy to install and highly effective.