Yes it can. High sugar can glycate the glycocalyx making cells be recognised as foreign thus inflammation. For example.

And in modern times many of us have chronic inflammation.

But I'd love if we found and focused on the injury/insult causing the inflammation rather than our bodies natural reaction to that injury. 

 Yes I understand that you would like this. But in some causes it is might the best part to eat less and healthy for lower inflamation. For example when the cause is alergies, diabetes or something like this where there is no faster way to treat them.