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Unless it's payments to yourself or gift cards, I'd imagine they'd increase your limit as opposed to lowering it.
I'm pretty sure that you will be fine. The Sapphire Preferrred is a Visa Signature which means the minimum CL is $5000. They can't offer anything lower in that format. As long as you pay off your balances on-time, it'll be ok.
I charged $7,000 on my Sapphire Preferred in the first month and they didn't seem to mind at all.