If you want to use it in one assembly it may be fine but using it over multiple assembly might be issue as custom property value would change for older assemblies.
You can rather create configuration in the file and can have different configuration for each assembly. Then you can control the property in configuration.
For a given part, you can select the BOM quantity. See File | properties, in the top right corner is a field called "BOM quantity". If you create a custom property, you can use this to tell SW to use it for BOM quantity (actually setting value by mistake is a common error). Now, for each configuration, you can have a "configuration specific" property that will be used. You can set this to the Mass by dropping down the Value/Text Expression box and selecting "Mass"
A word of warning, I recall reading somewhere that this is NOT always updated and that you need to manually run the Tools | Mass Properties dialog to regenerate these after changes.
If you want to get more involved, you could write a macro to fill property in using the GetMassProperties function or MassProperty object but perhaps that is not needed here.