Characters committed to quest can not make an escape test unless you ready them before the escape test comes up.
So let´s say you commit Eowyn and Glorfindel and Aragorn to the quest. You use Aragorn ability to ready him right away. You draw a treachery that forces you to make an escape test and you use Aragorn. Then you resolve the quest. All three characters count their willpower against the threat in the staging area. And at the end of the Quest phase you make the escape test for the Gollum card. If you have no characters left to use the test fails.
Longest answer I ever gave....I think.