I guess it could happen. My 6 month old was ABLE to sit independently (if I put him in a sitting position) from about 4 months, but maybe two weeks after he started staying up on his own he decided he NEEDED to crawl and as soon as I'd sit him down he'd roll over to a hands-and-knees position and rock. I didn't know how long he could sit for because he refused to do it! He was rocking on hands-and-knees or creeping every time he was on the floor until he started crawling at 5.5 months, and a couple of days after he figured out how to crawl, he went back to sitting up, except that now he could get to sitting on his own.
I introduced solids when my son made it absolutely clear to me that he was STARVING and not interested in more milk. I finally cracked the day he started crawling. I know, I know, wait until 6 months -- but this kid was READY and I silenced my inner opposition by saing htat if he can crawl, he deserves to eat. I hadn't seen him sitting independnetly for months but I knew he could do it (though I had the hardest time convincing him to bend at his waist to sit in the high chair) and in fact his first meal he scarfed down, feeding himself, half an avocado. So he was ready.