No, it doesn't. Every major airline publishes their fares, schedules, and availability in a standardized format; furthermore, all of this data is available from a single collection point. If Google wanted to allow international searches, they (or more importantly, ITA) already have everything they need.
They quite literally just need to "flip a switch" to enable it.
Most likely the reason they don't is that each additional origin or destination city that they add requires additional servers and storage and computation, and so it's much more practical for them to limit the tool to the top 50 or so Domestic USA airports.
If you've used flight search, you'll have seen that it's instant response. Change a filter on price, length of flight... anything... and the results instantly change.
The results are pre-computed... thus extending it to international flights is far from just "flipping a switch". It makes the pre-computation 1-2 orders of magnitude more difficult!
The schedules come from OAG, the fares come from ATPCO, and the availability (number of seats available on each flight in each booking class) comes either directly from the airline or through one of the three GDS providers: Sabre, Amadeus, and Travelport.
Technically, the schedules and fares are also available from the GDS, but only in an interactive format. ATPCO and OAG supply giant dumps of bulk data which is more suitable for offline processing and precomputing results.
Well, I'm sure it's a very nice interface.