Do any of the single player modes grant experience points or towards trooper challenges?

Solution 1:

Arcade mode does not appear to count towards Trooper Challenge unlocks, class experience points, or overall experience points. Though I'm not sure about campaign mode, the player always plays a hero for the most part in that mode.

I experimented with the kills, grenades, noted the class and overall experience levels and they remained unchanged after the arcade battles. Note some Trooper challenges say "In Multiplayer" and some do not, but all appear to require multiplayer to progress on.

Note the Time Challenge appeared to count the arcade kills, so that actually can be beaten in arcade mode. I also didn't measure Heroes so I'm not sure yet if the Arcade mode can provide progression for them.

I didn't test campaign mode because I had already completed it and didn't feel like testing it. Also some single player modes may add to the hero progression because when one receives cards it jumps up that hero one experience level.