There is no guarentee TN dealer will not charge you sales tax up front. If they do, they are "supposed" to send it to GA because when you register it in GA they will tax you then since it was a dealer sale. Make sure you keep the proof it was paid in TN if they do it that way.
Also the personal property tax will not be due in GA this year, but is based on who owns the boat on January 1, so you slide by on that tax. When you register a boat, your home county gets the info also and they will send you a notice of assessment next year.