The Anti-UN/UN Conflict from Macross Zero and the wider Macross Storyline is part of the plot, yes - it occurred around the same time-frame, and was the proving element for the early variable fighter designs, used in secret as the VF-0 and SV-51, alongside robotechnology-enhanced versions of existing fighters. 
There would have been some form of similar event to Macross Zero, maybe even with the Bird Human, but I'm not sure how it relates to things yet - but then, maybe even the authorities aren't sure of that yet either? 

That was probably the last major conflict between the two powers, as it occurred in 2009, after that things settled down into a relative peace, and the Anti-UN forces disbanded and became part of the UN Forces, which is why you have the mass-production SV-52 alongside the VF-1