As long as you have the time and location data consistent and accurate on every imaging or observation session, and as long the alignment data is intact, whether the data came from the GPS or manually entered, you will be able to achieve accurate GOTO's.
Although you can manually define the coordinates and time-of-day of your mount on your hand controller or on the PC (when using EQMOD), having a GPS device handy would allow things be done automatically for you. The location data may be fixed but the time component will not be as you are required to make sure that the time is accurate as the mount driver computes for the Local Sidereal Time (LST) based on the local time. The position of the stepper motor based on the requested RA/DEC Goto coordinates are computed based on the current Local Sidereal Time value.
Any electronic device (Notebook, PC, Watch, Clock, HC, etc) that maintain the current time will not be always accurate. You will have to sync it on a regular basis from a common timing system which can be found on GPS devices which are synced from an Atomic Clock passed to all GPS satellites.
A GPS would come in handy for mounts that are permanently located on a certain location (observatory, fixed pier, etc.). As you park and unpark your mount, the RA shaft position is usually memorized and the absolute position is computed based on your longitude and latitude coordinates and the current time-of-day / Local Sidereal Time.
With the GPS, the “continuity” of your mount “state of accuracy” is achieved. This means the data from any “alignment” operation/calibration done on a previous day can still be re-used on the current day and the days to come as you will be using the same coordinate data and the sky will still be “synced” with the RA shaft because of the atomic time.
If there are inherent discrepancies introduced on the time alone, that means you have to perform the same 1-Point, 2-star, 3-star, N-Point alignment every night for you to be able to maintain the accuracy on any GOTO operation.
In the EQMOD program code, the GPS data (time and coordinates) is processed even to the seconds/arcseconds portion in order to be able to compute in 0.144 arcsecond accuracy of the stepper motor position,
For mounts “on the go” or mounts that don't have a fixed location, the latitude and longitude coordinate and time-of-day data is usually important on the first alignment star GOTO coming from the initial home position. In the absence of an alignment data, the driver usually uses a “0” offset alignment. To “estimate” the position of the 1st, 2nd, and 3rd alignment star, it has to rely on these latitude/longitude/time-of-day data. This means, the centering process of any alignment operation would be better if your latitude/longitude/time of day are accurate. The GPS info would be helpful for this.
Some of you might ask are we still close to accurate GOTO's even without access to a GPS data. The answer lies on the different “offsets” applied on your goto coordinates. These offset data were derived from the alignment and star centering/calibration operation. The errors from the your latitude/longitude/time-of-day data are easily compensated by the star alignment operation.
However the accuracy may not be constant on all parts of the sky if you introduce errors on your coordinates as the accuracy will vary depending on which part of the sky your scope is pointed at. (unless you have access to an N-Point alignment). Usually the correction offset only applies to a certain part of the sky. (This where the N-Point and SYNC operation becomes handy). This happens as the mount firmware attempts to compute in a spherical coordinate system the location of the sky object. If your latitude/longitude data is not accurate, the virtual sphere which your mount firmware maintains to which your local sky is part of it will be a little “skewed” on certain sky locations.
At the end of the day, you get to minimize these errors and spare the mount from compensating these errors by simply using a GPS device.
Most mounts usually provide arcminute accuracy. However, with good command on programming, mathematical mechanics and depending on the capability and quality of the hardware itself, it is always possible to increase the accuracy towards the arcseconds level.