Normally it doesn't, but there's edge cases where errors can stack up and cause the entire layout to break.
A related problem happens in word processors: if you just layout and render a document at 1x, but at print time, you layout and render at any higher resolution; you will get a different layout. Lines of text that are just over the width of the page when rounded to the 1x pixel grid will be just under the width of the page at the higher-density grid of a high-DPI printer. This happens even at integer scales because fonts are designed on abstract grids that have no relation to (and are far finer than) the pixel grid that the document will be displayed on printed on.
(Complicating things, Windows intentionally renders fonts using custom rounding logic to force them onto the pixel grid as much as possible, this is known as ClearType. macOS doesn't do this nearly as heavily, which is why fonts look less sharp but more faithful on non-Retina Macs.)
AFAIK word processors either have to always round metrics down (so that layout decisions are deterministic at all scales) or always work on a 1x layout and render at higher resolutions using the 1x layout metrics.
A related problem happens in word processors: if you just layout and render a document at 1x, but at print time, you layout and render at any higher resolution; you will get a different layout. Lines of text that are just over the width of the page when rounded to the 1x pixel grid will be just under the width of the page at the higher-density grid of a high-DPI printer. This happens even at integer scales because fonts are designed on abstract grids that have no relation to (and are far finer than) the pixel grid that the document will be displayed on printed on.
(Complicating things, Windows intentionally renders fonts using custom rounding logic to force them onto the pixel grid as much as possible, this is known as ClearType. macOS doesn't do this nearly as heavily, which is why fonts look less sharp but more faithful on non-Retina Macs.)
AFAIK word processors either have to always round metrics down (so that layout decisions are deterministic at all scales) or always work on a 1x layout and render at higher resolutions using the 1x layout metrics.