Work, yes. People cross various state lines for work all time. FL has no income tax, but if you file taxes using your GA address you will need to pay GA income tax on your FL income.
If you actually live in FL, but don't change residency you're playing with fire. By law you need to change you to change your drivers license if you live in the state of FL for longer than 30 days.
Lived in NH, worked in Massachusetts for many years.