Yes. GDP tries to measure "production", it's just easier to add up various types of spending, investment, etc. But if the service has been consumed then it was - by definition - produced, or in this case the service was rendered, I guess.
That's why bubbles are a problem because they represent a misallocation of real resources. (Especially when they're debt fueled. And crucially so when it's private debt like the typical mortgage.)
But that's why the fiscal multiplier is above one, because public debt is usually cough spent on things that increase productivity, growth, or at least has a positive ROI (eg. regularly screening the mythical token at-risk individuals likely prevents enough very expensive private+public spending, and people will spend that money on things like education or mayhaps even just allows them to have more productive years), etc.
If a $1000 service was provided but not paid for, that's $1000 to GDP, and it was an expense for the person providing it instead of the person receiving it. It's as if you paid $100 to the hospital and the hospital paid $900 to itself. I think. Probably depends on the measurement methodology.
That's why bubbles are a problem because they represent a misallocation of real resources. (Especially when they're debt fueled. And crucially so when it's private debt like the typical mortgage.)
But that's why the fiscal multiplier is above one, because public debt is usually cough spent on things that increase productivity, growth, or at least has a positive ROI (eg. regularly screening the mythical token at-risk individuals likely prevents enough very expensive private+public spending, and people will spend that money on things like education or mayhaps even just allows them to have more productive years), etc.