I have a 'Gala' apple tree. Would planting a 'Granny Smith' tree in my yard serve as a pollinator for the other?

Yes, ‘Granny Smith” would be a good choice. If you can’t find a ‘Granny Smith’ tree, then a ‘Mollies Delicious’ would work well. To see a pollination chart for apple varieties, refer to this article on Pollination of Fruit Trees.