A11.6: "A leader may use his leadership modifier to aid any units in the same Location with their respective PAATC even if he does not advance into the Location himself." Unless it was clear from the "Pin Check" mentioned in A10.7 and the citation above, also using their leadership modifier to pass PAATC can be used multiple times in the same phase and in the same location. (And it clearly is an action.)
The principle is simple: You pick one action per leader per phase - but some actions enable to impart his leadership modifier on actions of several units, taken separately. So if you picked Rally, the leader can lend its leadership in the rally attempt of several units in the same location. If you picked directing a FG, it can lend its leadership to several of its attacks. This is valid for PAATC too. Then there are actions which can only be conducted once per phase; possibly because the leader is not directing but carrying them out himself. So the leader can only try to recover one SW per phase (RPh) irrespective of how many SWs are in his location, and it can only use the radio/field phone also only once and for one OBA "action".
What is an action? It is, for example, not clear whether lending his 1PP to an MMC is an action; though moving in the MPh certainly is. In principle, advancing should also be treated as an action - if a concealed unit advances into open ground in LOS of an enemy unit, it loses its concealment as a result of that action. So units advancing into AFV's location take an action of advancing, and that action requires succeeding at a PAATC check (which for those units taking the PAATC check does not count as a separate action, it is part of advancing). However, for the leader the action is commanding the MMCs taking the PAATC, i.e. imparting his leadeship to their PAATC attempts, and he just "joins in" on their results. This principle of "joining in", when leaders become kind of like attachments to an MMC that carries out an action under their leadership, are also apparent in how a stack is marked with counters in PFPh & MPh/DFPh (i.e. including the leader), joining of broken routing units and participation in close combat, and I guess we could think of more. So the leader does not conduct two actions of directing the PAATC and advancing. His action it to direct the PAATC, and the action of the MMC is advancing (conditional to the PAATC result), on which the leader can participate "for free", as a result of directing. If such a stack advances into open ground, it loses its concealment as a result of that action, and the "joined in" leader does too even though formally his action was directing the PAATC.
The takeaway is that there is a distinction between a unit taking an action and a the action of a leader directing an action of another unit (and partaking on its results "for free", i.e. not as a separate action).
With that out of the way we just need to think through whether the formulation "freely at the start of the phase" implies an action or not, absent any other ruling.