No, never.
*IF* The anarchy faction in question owns a port where you can turn in boutnies, superpower bounties of Federation, Alliance or Empire can be turned in to boost the influence and rep. Provided you can turn them in there... it will requires a relevant aligned minor faction in the system to be able to do so.
Hmm not sure that still works - I think super power bounties only affect super power rep now.
I got burnt trying to move influence from one system to another by combat bonds (cashing in at the non-war system). It just boosted the system the CZ ws in as of 2.2 (or whenever the remote bounty,fine etc. system came in).
Tuffy when there is only 2 factions, however it does makt 100monkey's suggestion easier to implement. Go kill the controlling factions ships (yes you will ose rep for this), but it will directly increase the anarchy's influence, icreasing the chance fo missions. On another note if you kill wanted do not hand in the bounties!
Simon