I'd like to examine how Eve mechanics make this--a new player being useful to endgame players-- possible. There some obvious reasons, but also some subtle mechanics in play. I don't play Eve Online currently, so if I make a mistake with mechanics, please correct me in the comments.
1. No Maximum Group Size
The obvious mechanic is that Eve does not cap group size. You can take as many people as you want in your fleet. Thus taking a new player does not mean benching an experienced player. So you can take pretty much everyone to a battle.
2. Bounded Accuracy
In most theme parks, your chance to hit decreases as the level difference increases. Usually at a certain point, a low level character simply cannot hit the high level, and so is pretty much useless. In contrast, Eve pilots can always at least hit the enemy target most of the time. A new pilot might not do much damage, or be restricted to holding the enemy in place, but at least her abilities can connect.
3. Opposition Does Not Scale
The opposition in Eve does not scale. So bringing an extra player does not make the fight more difficult. It always makes it easier. If the opposition scaled, there would be a point below which bring lower level people would be a hindrance, would make the fight more difficult.
4. No Area-Of-Effect Attacks
This is the subtle mechanic, but in some ways it might be the key one. Eve is a single-target game with very few area attacks. I believe the few area attack weapons damage both friend and foe. The usual targeting mechanism is select a specific ship, lock on, and fire guns.
If you think about it in terms of global cooldowns, killing an enemy requires at least a GCD. That's one GCD not spent on attacking a different player. In PvP games, the priority targets are a function of the ones with the weakest defenses and highest damage. New pilots have very weak defenses, but very low damage. Most of the time, it is simply not worth the GCD to target a new pilot.
This allows new pilots to have pretty decent survivability, even in fights with much larger ships duking it out.
On the other hand, if ships had a decent AoE attack, a single AoE pulse might wipe out all the small enemy ships. Spending a GCD to kill several small ships at once might very well be a worthwhile tactic. If this was the case, there wouldn't be much point to bringing new pilots, as they would get AoE'd off the battlefield within the first few seconds of the fight.
Those are the four mechanics that I think allows Eve Online to have its new players be (theoretically) helpful in high level combat. In my mind, the first three are fairly obvious and could be implemented in theme parks in a straightforward manner if desired. The last one, though, is subtle, and has many ramifications. AoE is surprisingly important to Trinity gameplay.
Of course, I should note that just because Eve Online mechanics allow day-old pilots to participate in combat, that doesn't mean that most newbie pilots will ever see such a thing. From my experiences in Eve Online a while back, most corporations are so scared of getting scammed that they won't invite new pilots unless there is an existing out-of-game relationship to verify them.
It’s great that the mechanics allow this gameplay. Too bad the politics will make it inaccessible for most.