I'm thinking there must be a study somewhere.

And indeed there is, where they studied people who were born just before and after the end of WW2 sugar rationing in the UK:

https://pubmed.ncbi.nlm.nih.gov/39480913/

Those people are into their 70s and 80s now, so the long term health outcomes are well documented:

...we found that early-life rationing reduced type 2 diabetes and hypertension risk by about 35 and 20% and delayed disease onset by 4 and 2 years, respectively. Protection was evident with in utero exposure and increased with postnatal sugar restriction, especially after 6 months, when eating of solid foods likely began. In utero sugar rationing alone accounted for about one-third of the risk reduction.