Obviously, everyone will be different but I get 2-3 emails from recruiters on LinkedIn per week. Managing them takes me about one minute per week.
Compared to the number of times where I ended up on a phone call or having lunch/coffee with a CTO, VP of Eng, architect or senior engineer, it's totally worth it to me.
My suggestion: don't cut out that option until it really becomes unmanageable. Chances are you'll find it's worth the occasional disturbance.
You have zero pressure, you can practice interviewing, network and you can make extravagant requirements. If it doesn't work out, no big deal, you like where you are. But if it does, your career can make quantum leaps.
In other words, a $10k increase in salary might not seem much but it will add up, and not only will raises compound as well but future jobs will start at a higher negotiation level as well.
Of course, spend your time wisely but I think it's really short sighted to think "I'm happy at my job, I am going to completely block out all the recruiters out there".