"That" thing is precisely the power of idealism. Compare Antonia's line,
"Why should any one of us think his aspirations unrealizable?"
In the case of Decoud, who usually argues the futility of everything, the key
word here is "would." With this "would" the sentence seems
incomplete, missing an "if" clause at the end. What is Decoud's unspoken
finish? For he obviously does not carry a belief in "the feasibility of anything"
for very long. It perhaps has something to do with his careful, self-correcting
distinction of "brain" and "heart" in the next sentences.
He loves Antonia (idealism) with his heart, but his brain is merely set "on
fire" by her, which could be read as the agony of contrast between his love
and the intellectual skepticism he still holds. "If" his heart and mind
could unite, Decoud might learn to believe.