Yes, why? All good advice. I have killed many a small rooted fig this past winter by over-watering!
Figs are flexible but they do not like sudden changes, even something as simple as putting them out into full sun. Generally speaking the plant will establish the right relationship of leaf growth to root mass *after* it is well established.
If those wilted leaves really become dry & papery (tomorrow?)...you will have to cut them off, resist the temptation to over-water, find a way to get more air on those roots, & it should come back fine.
Once it is well established in semi-shade (weeks?) then full sun should be ok?