Does the existence of a production pie demonstrate the existence of aggregate demand?

Assuming "demand" is defined as an economic force created by people with purchasing power pursuing goods sold at their market value, then increasing the money supply will increase demand (assuming money gets into the right hands), creating a shortage, and increasing prices. This will, in turn, shift the production pie to meet the new demand.

Witnessing the production pie shift with changes in the money supply gives us evidence of this aggregate demand.

I think it sounds like you're talking about the effect of expansionary policy on production via a mechanism that doesn't involve demand, but rather where investments go. Wouldn't this suggest a mechanism whereby monetary policy can affect production without any reliance upon the concept of aggregate demand?

It would, if you could decouple available production and attendant price from demand for products. Ultimately, however, if you increase investment in car factors and produce a surplus of cars, you're going to drive down the price and increase the ability of would-be drivers to purchase new vehicles. People who are now buying cars will be less likely to buy metro-passes or bicycles, while premiums on parking spaces will rise. And that's due to limits on the population. Everyone needs to travel, but there's an upper bound on the amount of travel one can reliably consume.

In the same vein, investment in apples which make them cheaper than oranges will increase demand for those apples and (because people can only eat so much) decrease demand for oranges. You can do this with any set of replaceable goods.