Yep I've got one too, but they don't tell you the real heading...
No, but it is good enough. First, if you are trying to get somewhere, you don't stop. (Hard to stop an airplane
) If you are moving, the GPs can figure out the instantaneous bearing to the waypoint, and the heading you are on.
If you are not on the correct heading, the bearing to the waypoint will be changing slowly, as will the cross-track error, which changes very fast. The goal is to find a heading (upwind, to correct for wind drift) that just offsets the wind drift, and keeps the cross-track error from growing.
I do this every time I fly some where. I have a pretty good idea where the wind is coming from, and its speed. From having done it thousands of times, I can usually guess how much correction it will take. If I guess wrong, and put in too little correction, I can tell within a minute or so that I need to increase it by 5 or 10 deg.
Now I grant that when I'm flying, I'm watching the Directional Gyro (slaved to magnetic North) at the same time I'm watching the GPS. I fly a magnetic heading, and the GPS tells me if that heading will get me directly to the waypoint. If the cross track error is growing, I add/subtract 5 degrees more/less wind correction at a time until the cross-track error stops increasing.
I have been doing this a long time. The early version GPS (and Loran) navigation systems updated at once per second or less, and updated too slow to maintain a heading without using the DG (compass) between updates. The current crop of GPS update at the rate of 20 times a second, and at that rate, the GPS derived heading information is more than good enough to steer a course without looking at the DG (compass), even in an airplane traveling 170mph.
I know that there are GPS Steering systems that work without using a separate heading indicator and there are others that use an output from a directional gyro as well as the NMEA from the GPS. Pre-GPS autopilots used an inductive pick-up from the card in a Directional Gyro to steer.