I'm not 100% sure whether this should be possible, but it would appear to be within the rules.
I tried to set a board up that has the Augurs (indicated by the Herb Gatherer) as the card for the Way of the Mouse.
Although the Herb Gatherer appears on the list to select, if I select it and attempt to start the game, red text appears saying this is not a kingdom card. Please see attached screenshot.
Split pile cards from Empires (eg Catapult) can be selected, but testing with the other Allies cards it seems non of the Allies split cards can be used in this way.
Is this a bug, or have I missed a rule somewhere?