Possibly, but it's not a simple thing.
You can "scrape" data from a data viewer--which can be used to access google maps to get the mileage, but you get a mass of text and html tags and have to use fairly complex text functions to locate and extract the data.
Look up GetLayoutObjectAttribute in FileMaker help. You can give your web viewer an object name and then use this function to extract the viewer content. Then the fun begins--analyzing the resulting blob of text to figure out the needed calculation to extract the mileage. If you decide to take this on try using this function with a set field step to dump all this text into a large text field where you can look at it an try to figure out an expression that will successfully find and extract the mileage figure that you want.
I haven't tried using it myself, but if you are using FileMaker 12 (I forget if you are or aren't), there's a new function in that version that may make extracting this initial mass of text easier.