My employer is based in GA but has several national projects which place GA residents traveling and working in different states more than half of the year. Does the employee who has a home in GA but works in a different state still complete a G-4? Would they also need to complete a tax form for the other state in which they are working? Thanks for any clarification on this?

If you work (or work and live) in two different states, you will file tax return in both the states. One state is your tax home. In the state that is not your tax home, report income you earned while in that state. If you have received only one W2 from your employer, then use simple arithmetic based on number of days spent in the state to figure our the income that you should report to this state.
In the state that is your tax home, report your worldwide income for full year. Also in this state claim credit for the taxes paid to the other state. Your U.S. Tax Return: Working or Living in Two or More states