Debt-to-GDP ratio in connection to inflation
The premise that a high debt-to-GDP ratio will imply higher inflation is questionable. If we look at the data for the United States, there appears to be a negative correlation: the ratio was lowest in the high inflation period of the 1970s to early 1980s.

link to FRED graph

As hinted by your question, growing the denominator (nominal GDP) lowers the ratio.

Unless one believes in the Fiscal Theory of the Price Level (described in other questions), there is no obvious link between the debt ratio and inflation. 

If we drop the focus on the ratio and look at government spending, we arrive at the theory of Functional Finance: the constraint on government spending is inflation. That is, we need to look at the size of the deficit, what the government is purchasing now, etc.; the debt ratio just tells us about historical spending.

Link to Kelton article on Functional Finance.

It looks like your question is really about the validity of Functional Finance, but you have written it up as being about the debt-to-GDP ratio.