Short answer? Maybe.
As shown in this video made by the Provence winery Mirabeau, it's certainly possible (for wines sealed with a cork):
But if you've tried to do this in reality you'll know that it is nowhere near as easy as it looks.
Here at The Tasting Glass we've given it a red-hot-go several times now and can confirm that unless you have shoes with a firm soul (like dress shoes) it simply doesn't work. Ditto if the heel of the shoe isn't reasonably even (so sports shoes with tread are no good either). Further, it doesn't work with cheap plastic corks and many conglomerate corks too.
What we have worked out, however, is that you don't even need to use a shoe at al. Rather, if you just line up a wall/floor/door/any hard surface at just the right angle you can open a bottle that way. All you need is a constant rhythm and a little patience.
So what are you waiting for? Grab a bottle and try it for yourself!
(Photo by Quinn Dobrowski)