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No experience with the Z1, since I Installed it yesterday but it most likely is programmed to follow roads.
I have two different garmins so I have to assume the Z1 will follow my on-road Garmin. It is set to follow the road since there will be some variation between the actual position of the vehicle and the road; primarily due to the maps being slightly off. The software will then put your pointer right on the road.
My handheld Garmin 60csx, which can be loaded with street maps, has a setting to show on road or off road. While traveling to Utah, I pulled it out of the luggage and set it to follow off-road. It showed that I was about twenty feet off of I-80, to the right of the shoulder. When I switched it back to on road, I appeared on the road.
However, if you are a specific distance from the road, all should show exactly where you are. So, I have to assume if you are traveling a mile from a road, in the desert, it will show where you are.
Unless you have topographical software that shows trails as well as roads, it may just show that you are in the middle of nowhere, if the software can show a trail, it should show that you are on a trail.
The Z1, to my disappointment is only an 8-channel GPS receiver, that is it can only obtain up to 8 satellites, and it does not state anything about the wide angle augmentation satellites (WAAS). With the software, it is probably great for navigating the roads. Since the GPS satellites can transmit information that is slightly off, the triangulation of your position can be incorrect by a few meters. The WAAS system uses satellites to send out correction information, which allows the GPS receiver to obtain greater accuracy.