If you have enough hours, yes. Although, I’ve know some managers rule against sick time for almost anything.
As per the handbook, sick time can be used for any missed work due to illness or injury. Recovery is due to it so technically. Also no point in working when recovering cause you’d be backtracking.

If it’s going to be two weeks though, I’d recommend calling Sedgwick (if in US) and request a medical leave of absence ahead of time. Give them the dates. They just need medical notes from your doc. and a note saying no work (even limited) during recovery time.
Medical leave PAY begins seven days after first date of work missed (iirc, there may be an exception where it starts first day if surgery or hospitalization). The Sedgwick rep. will give you the full details.

In short, medical LOA will pay you 66% of your average hours worked for the past 26 weeks (iirc). It’s in the handbook. So you can save your sick time and/or use it for the 7-day unpaid period mentioned above unless it’s that exception.

One point to mention, during this time you’ll be employed by Starbucks but paid by Sedgwick. You’ll receive a second W2 tax time, and if you have medical insurance with Starbucks, you’ll get a bill in the mail to pay it as you aren’t getting a check from them to take it out of.

Hope surgery and your recovery are swift and safe!