A useful way to re-frame this question might be to ask yourself "which principles?" What do you think unschooling is or does that can intersect harmoniously with the life of a schooling family? There certainly are aspects of unschooling as a philosophy that can have a place in virtually any life, because they're principles of human nature and relationships that people have explored for centuries. The only thing really special about unschooling is extending those principles of human nature to children.
One of the fundamental principles of unschooling is that people (including children) are naturally curious. Teaching can dull that, true, but even school kids are curious - in school that's just called things like "being distracted" or "inappropriate socializing" You can support your child's natural curiosity at home by stepping back from schoolish assumptions about how learning "should" look and instead see how it really happens. Which may include socializing with friends, playing video games, and watching tv rather than glamorous poster-child activities.
Valuing socializing and goofing off are also important because people are naturally social - we frequently like to learn from other people - and natural learning itself is mostly enjoyable. Applying those principles at home, with a school kid, means looking for more ways to connect with your child, and to have fun with your child. It means looking for ways to both invite your kid into your adult life and find welcome in your kid's life - which can be difficult if you've gotten used to connecting over school and homework and otherwise expecting your kid to "go play". It can take some stretching and softening to learn to enjoy some of the things that light your child up.
One principle that adults tend to like in theory but struggle with in practice is that it helps to be open to a spirit of enquiry. We struggle with that because we want to direct it with leading questions, Socratic, and outright criticism of kids' natural interests - all of which tend to shut down enquiry if they're the main mode of interaction. The occasional Socratic question isn't a bad thing, but there was a reason people didn't like Socrates Creating lots of projects that lead kids in the direction you want to go is more of the same. It's all back-door teaching rather than supporting natural curiosity.
But the other most fundamental principle of unschooling that anyone can use any time is that thoughts and feelings matter. Specifically the thoughts and feelings Of Children matter. They matter to learning - they have a direct effect on what is learned in the moment. They matter to relationships. Taking your child's thoughts and feelings into account, taking them seriously, and being mindful of children as people is the heart and soul of the unschooling philosophy.