Taxation for a foreign entity set up as a single member LLC with an s corp selection

[ss]

I have a single member LLC with an s corp election formed and  registered in NY.

I'm in the process of changing my primary residence to Georgia, but expect to return to NY in the next few years. Given these circumstances, I'm thinking of registering as a foreign entity in GA rather than dissolving my NY LLC and forming a new one in GA. 

I realize I may responsible for some fees/paperwork in NY, but if I establish a foreign entity in GA, can I change my business address/location to GA (for payroll purposes) and pay all of my payroll and income taxes through GA (my primary residence)?

Thanks for any assistance.

[Anonymous_]

@Mike9241