It's a major hazard, you would not believe how many ways authors find of simulating a degree symbol without using the actual symbol, usually superscript '0', 'O' or 'o' but they find others.
In fact one of the main tasks in preparing text for publication is stripping out all the formatting carefully applied by the contributors to make the text as 'vanilla' as possible as the designer essentially needs plain text so when they format it nothing odd happens. Also have to elkimate double spaces, redundant LF/CRs…
So, by the time they find there way through word, indesign and acrobat any clever symbols are probably going to wrong.
Neil