No, grid lines are country or region specific and only usually available on fixed resolution maps; our maps are not a fixed resolution and are not datum specific. You can use whatever datum you want (that the Garmin device supports) and that datum will be used on our maps.
Grid lines are of limited value on such maps, as you can always get the current grid reference from the Garmin device (using whatever grid system you prefer, or is designed for the country/region/area you are using the device in). Using the wrong/incorrect grid system is dangerous as they are designed for fairly small areas of the globe and quickly become useless near the edges or beyond the area it was designed for.
As an example British Grid is not suitable, safe or designed for use outside Great Britain, if you try to use it in Italy or even France, the reported grid reference would be up to hundreds (or more) of meters out.
Once you have the grid reference it is trivial to compare this to a paper map that uses a specific grid system.
If you are using devices and maps all over the world you would be better off setting the device to WGS84 which is a global standard for longitude and latitude co-ordinates. WGS84 is as accurate in Hong Kong, Peru, Antarctica, etc. as it is in Italy, the British Isles, Bulgaria, Canada and the US, and so on.
There is a knowledge base article on map Datums that are supported and which you should use, here.
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