Of course! Advanced degrees aren’t a prerequisite to publication. Daniel Handler, more widely known as Lemony Snicket, and Amy Tan, who wrote The Joy Luck Club, are two contemporary authors who have published without an MFA degree. There are many, many more.
Excellent writing snares a publication deal, not education credentials. MFA programs certainly do have benefits. They provide a community of people who value writing, plenty of guidance, and opportunity to discuss literature and craft with established writers. MFA programs also provide a writer with time—a precious commodity. Still, an MFA isn’t a sure ticket to publication. And not all writers need an MFA program to hone their craft. Some focus on self-study, reading, or workshops with writers’ groups to improve. Publication comes down to strong and engaging writing, no matter how you go about getting your work to that level.
One thing all writers must do—whether working toward an MFA or not—is practice, practice, practice. Then, they practice some more.