The Liberty Navy's first and foremost objective is to protect the economic might of Liberty.
That said, I doubt the Navy, or the Liberty Government would get involved in anyways unless their economy will be affected.
Since the Bretonian Government is paying, by themselves, any ship that takes refugees out of their systems, this could be a good economic venture for the Libertonians, but if the Liberty Government tries to profit from this, they could easily be accused of trying to profit from war. Also, Kusari might not want to let those refugees go because they may consider them their own citizens, once Leeds is captured and all.
If Liberty does decide to begin investing in the rescue of refugees, this could create problems if a Rheinland trader, or even possibly a Rheinland Government chartered transport comes in contact with the Libertonians in Bretonia.
If Liberty does chose to 'profit' if you will by rescue refugees, relations with Bretonia and Rheinland could boil, as Rheinland could accuse the Bretonians of supporting the war effort against Rheinland too much, since the funds acquired by the Liberty Government from rescueing the refugees could very well be used in the war against Rheinland.
The way I see, if Liberty wants to rescue refugees, they may have to make a deal with the Bretonians that they will do so without profit (in RP of course).
As for a 'Peacekeeping' force, doubt that would happen, there would, by a minimum, need to be a ceasefire in effect with Bretonia and Kusari, which doesn't seem possible at this stage. Even if there were, Liberty's resources would need to be directed against Rheinland, even though they out gun Rheinland by 2 - 1 Rheinland still poses a serious threat since unlike the Colonial Remnant, it is a superpower.
The only way I see Liberty joining the war against Kusari would be if the economic situation in Bretonia gets so bad it begins to affect, greatly, the Libertonian economy. Of course that would come at a price since they wouldn't be able to trade with Kusari anymore.
Honestly, I doubt Liberty would interfere with their war, but this is just my opinion, other Libertonians may disagree.