Why is it any different if the government takes out a loan to pay for work instead of someone like GE doing the same? If someone takes out a loan, and then spends the money building a plant or hiring employees, the economic activity is real..
It's the age old problem of once you choose the system of measurement, it's going to get manipulated by the people who get measured by it. GE is not going to rack up a bunch of debt for the explicit purpose of making sure the GDP number goes up. When the government creates a bunch of money just to make sure the GDP number goes up, GDP stops being as useful at telling you how things are going.