Entirely.
At my co-op job (just graduated in May) we hired for summer starting in spring semester. If you start prepping now you can start applying day 1. Companies who know the internship schedule will post at the beginning because they want the most time to screen applications, even if that means doing 2-3 interview days on campus. The other upside is that you're not crunched for interview schedules. It's not unheard of for Google to get back to you a few weeks after you applied, or even after you past round 1.
If you start applying in spring, you also have the option of starting in fall if that's your initiative. This would probably fall more in the co-op category than internship. This lets companies overlap you with another graduating co-op. If their schedule is summer, spring, fall, you could want fall to overlap. Or if they do 4 terms it's summer, spring, fall, summer.
From experience, our interview pool sucked in beginning of fall, so don't apply for spring term if you can help it. We would interview in fall for the upcoming summer sometimes, but most of the time we were trying to hire to replace the students who stayed 5 or 6 terms. We found that it was mostly (though not entirely) rejects from spring hiring that couldn't find a job in summer and didn't go to school over that past summer. As a result of this happening for several years in a row, we stopped having on campus interviews in Fall, though if you applied to us directly we would interview you.