Residency renewal issue (Istanbul)

Hello all,

My residence will expire on April 13 so I decided to make my renewal appointment this Monday only to learn that the earliest available application date is June 24. I had been planning to be out of the country for a week from May Protected content I hear this may make trouble trying to re-enter the country. Since I have already bought the tickets and have not had a vacation abroad in nearly three years, I do not want to cancel the trip.

My question is this, would it be possible for me to leave between now and April 13, come back in on a tourist visa and then use the tourist visa for my May trip? PS I have an American passport and have been resident here for around 4 years.