Can 12 Gauge Strings fit on a Floyd Rose® double-locking tremolo?

I bought a Jackson guitar (Slat 3-6 Soloist with EMGs) and I'm going to have it set up for Dropped C Tuning and I want 12 gauge strings to accommodate the tension of 10 gauge in standard. Can 12's fit?

I have a Razorback with .13s. The only issue I have is an unwound third string doesn't stay in tune too well.
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