Q: Wouldn't the open-loop equation changed somewhat
for the self-biased PLL based on Maneatis design
since there is no actual resistor?

Look at Maneatis' paper in JSSCC Nov 03. In place
of R, use 1/gm where gm is the transconductance of
the element he uses in place of the LPF resistor.
Note that the 1/gm is not constant with PLL frequency
since gm is dependent on sqrt(Ibias) and Ibias varies
with frequency.