We did see Aran'gar use compulsion on Ramshalan at Graendals request in ToM. And Ramshalan did act pretty normal after that, suggesting that Aran'gar is not totally incompetent when it comes to compulsion. Granted, Rand balefired her pretty quick so we did not get to view Ramshalans behaviour for long, but Graendal atleast thought that Aran'gar was skilled enough to construct complex and convoluted compulsions and Graendal would presumably know best.

I don't think it would make sense for there to be any major compulsions in Egwenes mind (since as you say, there is no struggle), but I could see there being subtle commands there that are affecting her judgement.

Things like:
- Oaths are important and vital to beind an Aes Sedai (benefit of reduced combat ability against human darkfriends)
- The Dragon Reborn/Asha'man are dangerous and should be distrusted (obvious benefit)
- Enhanced fear of Seanchan so Egwene won't send sisers away from the tower to fight the trollocs in the borderlands but will keep them in Tar Valon to protect the tower.
- And so on. Basically, just enhancing thoughts/emotions already present might have helped shadow in some ways. Even very weak compulsions like the ones Verin used can have significant effect.

There is also the possibility of somekind of hidden trigger in her mind that is dormant and waiting, so if Aran'gar says/does something, that hidden compulsion kicks in to do something. Thoug I am unsure if this kind of "post-hypnotic suggestion" is possible with compulsion.