It wouldn't have "real" bonuses, but depending on the illusion you can give it all the magic you like. For instance, major image allows for thermal effects, so you could create a flaming greatsword that would give off heat. Also, you could have the image not break when being hit with a magic sword, so it appears to be a stronger magical blade.
Depending on what you do can make the image more or less believable.
Well, being that it's not a real item, any attempt to enchant it, by default, fails. Just as you can't really kill an illusionary orc, you can't enchant, break, or steal an illusionary sword.
However, the caster is certainly entitled to PRETEND to enchant the item, and pretend that the item has been successfully enchanted, if somebody else thinks it's a real weapon and tries to enchant it.
For normal illusions (glamers, patterns), no, there's no physical substance there to enchant; if someone fails the save they may THINK it's real but it still isn't.
Shadow spells, on the other hand, are a different issue. They actually have a physical substance (20-60% real), so you should be able to cast spells like GMW on them.
You could try to put a straight +1 enchantment on a shadow sword, but you'd have a problem making an illusion that lasts the minimum 1 day it'd take.
(Closest geek analogy to shadow matter: Star Trek Holodecks)