Wrong, it gives immediate benefits of extremely high sustain due to the on level heal/mana restore until around level 10ish. Bot lane can finish RoA by 5m and have it maxed by 15. Any normal game will last at least 20m.
p.s. they also give u mana
u know what also gives u sustain? the dominion aura
u will never need more sustain than that. if ur low on hp/mana, roa wont help u. its not something u can activate on command.
and maxed at 15 min? the game is basically over by then. u'd need a pretty epic comeback to pull off a victory if ur losing at the 15 min mark (unless ur playing against a really bad team i guess)
u know what happens before the 15 min mark? ur opponent builds items that help him right away and simply dominate your lane. u know what happens when an opponent dominates bot lane? they control both their point's health relic and the relic in the middle of the lane, giving them sustain as well as the item advantage.