This hasn't held up at least over the last 15 years ago in the US. Our debt to GDP was around 60% going into the housing crisis. The ratio is now roughly twice that, around 120%.

In that time our national debt went from $9B to $33B. GDP went from $15B to $25B.

You can always calculate the multiplier, but in this context the multiplier would really need to be greater than 1 to show a meaningful economic benefit to the additional spending, and the debt to GDP ratio would decrease as GDP would grow faster.