Is is in any way possible to determine if my opponent is in a higher/lower or same league as myself while I'm actually playing against them in 1vs1 in starcraft 2, or am I forced to check this after the match is over?
In theory if you had a person's user name and number, you could look them up (on the blizzard website). Unfortunately those numbers are hidden by default so unless you get your opponent to give you his number, I don't see how.
Ultimately I tend to ask my opponents, and I find this works well. I can probably trust their answers about as well as I can trust them to give their hidden number.
More often than not, I can tell a person's league just by scouting:
These rules aren't hard and fast, but they do tend to explain 90% of my games.
If I'm getting 4 Gate timing push at 6:30 you can bet the guy is in diamond.
Where this breaks down is when you start to get top 10 diamond and then start seeing things like: bunker push, 2 pylon wall in. And all of a sudden I start sweating...
I don't know of any way to check this ingame, but i wouldn't recommend it anyways... you need those APM you would use to check his league to beat him.
Short Answer: No