It seems to be enough to have an adequate avg Ilvl including any items in your inventory.
So in case you dont want to break a set/loose some special item while leveling just keep random blues in your bags and ilvl should be no problem.
To add to this, the blues have to be equippable(aka no Plate Items, but str/agi neckpieces/rings/cloaks are fine). This leaves clothies at the biggest disadvantage in terms of getting the requirement to get into the heroics, but its better than nothing.
For reaching the heroic ilevel threshhold, don't forget about pvp gear. I had some extra honor left over from WOTLK, which I used to buy a new pvp trinket. You don't even have to wear it to raise your ilevel. The pvp gear is particularly useful for this because the blues are a high base ilevel.