It is possible, and I've known quite a few people who do it (as well as many, many people who worked in jobs over 2L summer that didn't guarantee offers afterward, like PD and DA offices, etc. and just plain need a job). You probably won't find as many large firms hiring 3Ls since many fill their needs in their summer class, but even these firms have people turn down offers or take clerkships, etc. And many small and mid-sized firms hire too.
You can definitely look for a different jobs, and hopefully you'll have an offer from this summer as a safety net if you need it. Good luck!