Can ilvl 59-60 items compete with ilvl 61-63 items?

Like you said, all gear that is dropped going forward will roll based on the monster level, rather than the item level.

This means that, at Monster Power 0, all items in Act 1 are effectively ilvl 61, Act 2 are ilvl 62, and Acts 3 & 4 are ilvl 63.

At Monster Power 1 and up, all items dropped in Inferno are ilvl 63. Period. The only difference is the base armor or damage that rolls on armor and weapons. If you're looking to maximize your armor, then, yes, you'll still want to only pick up Archon armor. Otherwise, as long as the monsters are level 63, just hoover everything you can get your hands on. Since jewelry doesn't have inherent armor or damage, iLvl is now a useless stat for it; an iLvl 58 (minimum Inferno level) amulet can potentially be as good as an iLvl 63 amulet.

For weaponry, though, you may want to be more picky. Since weapons can roll +% damage, they get a bigger bonus from the higher base damage on higher item level weapons. Overall, though, the difference between an iLvl 58 and an iLvl 63 is going to be minimal.