I say no.
A lifestyle is the way you live. It's a thread that runs through every part of your life: You eat it and sleep it. A lifestyle is both an environment and a mindset.
Most people live a life, not a lifestyle. That's true for kinky folk, too. With rare exceptions, BDSM is just a way of interacting, a sensual hobby, a sexual game. But saying "we live the BDSM lifestyle," sounds hipper, more alt, more extreme, than "We enjoy BDSM activities". The expression lends extra drama to a part-time endeavor.
Indeed, the "BDSM lifestyle" phrase is generally overkill; it's also pretentious and "cooler than thou."
Nobody ever says they live a "parenting lifestyle", although life changes drastically when you become a parent.
It's time to drop the "BDSM lifestyle" expression.