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The adafruit GPS is a very accurate GPS module. But you use it with your cellphone to send the coords to Arduino? Using GRPS is horrible. It is not accurate to calculate the position. And it is very slow.. Can you tell me the name of the compass you are using?
Maybe i can help you out whit tis.
Yes it is possible. I did some coding, and my car follows a path of waypoints to reach the destination. And it is very accurate. Only you need is the right GPS. I prefer the u-blox 6M NEO GPS. It is a cheap GPS module. But very usefull. Its cheaper then the Adafruit.
It is a shield. But you can do it whithout GPS shield and use another Motor shield like the L298N. And Ublox 6 NEO GPS module. Its cheaper, and you have a lot more space on your arduino Mega.