I agree that the difference you are aluding to exists, e.g.
TrotzDEM ich starke Kopfschmerzen hatte, bin ich zum Training gegangen."
(i.e. in the meaning of
obwohl as you said)
"Ich hatte starke Kopfschmerzen,
TROTZdem bin ich zum Training gegangen."
(here you could use
nichtsdestotrotzinstead, or also
trotzdessen, contrary to
trotzdem you wouldn`t make a difference in accentuation though).
The first usage however is quite antiquated and isn't used often in today's german.
As for a part of your question, if someone uses it that way (or other words for which such a difference exists), you'll probably catch the difference rather intuitively based on context and sentence structure (altough the differnce in accentuation is there too). I think catching it based on accentuation alone would be difficult (depending on dialect etc.) even for native speakers. I agree with @Emanuell's comment however that the it will sound weird in the first example if you use the second accentuation.
Right now I can't think of another (more modern) example of a word that has different meaning based on accentuation, but I'll try to think of something...