That's a little condescending. Just because I've reached a different conclusion doesn't mean I'm blind, asleep, or otherwise not seeing things clearly.
No, she can't. When you grant actions, you aren't taking or performing those actions. You're allowing others to act in your place. When you do this, you're not attacking. You're not even the one in the spotlight because you're foregoing the ability to do anything on your own so someone else can act off-turn.
Heck, the party actually loses action potential. Without action granting, your ally could still take that action on their next turn, and you could act on your turn. With action granting, your ally sacrifices a reaction to act earlier and you lose the ability to act on your own. The party is, net, down a reaction just so someone else can act in the warlord's place.
Another way to think of it is like this: the warlord effectively uses her action and burns the reaction of an ally to summon a creature who's an exact copy of one of her allies to perform an action and then immediately disappear.
That character isn't fighting like a fighter. That character is non-acting and burning an ally's reaction to have an ally take a prescribed action.
You're also looking at things in a vacuum. For example, my idea for the warlord would prevent the warlord from maintaining concentration when granting actions. My premise for this is that the kind of battlefield awareness a warlord has to have in order to grant actions requires an amount of focus that precludes concentrating on spells (or on magical item effects that require concentration to maintain).
Chaotic evil schutzstaffel fighter ally?
Again, condescending. Plenty of things are bad ideas.