Yesterday afternoon I did just that and I get a trendline with an equation of y = 3E-08x2.8413 which suggests scaling will be a problem.
Can't sleep :(. Just realised I was using the wrong values in my chart. The number of edges was actually the square of the values I put into the chart. I'd designed my test polygon by creating a square filled with horizontal squiggly lines designed to maximally stress the vatti algorithm (since it results in a near maximal number of LocalMinima with left and right bounds all of length 1). Anyhow, reworking the data with the correct number of edges, the equation for this (near worst case) test polygon returns an equation of y = 1E-08x^1.4821 . If I generate the squiggly lines vertically in my test polygon (and destress the vatti algorithm) which is likely to be closer to normal use, I suspect this equation will drop further. Will leave that till the morning.