Is ripple of LC filter constant?
simply put, it is not independent of load, during design you tend to consider the load as a resistor and usually just affects where the system will stabilize and it is most cases the final result not far from this, at least from my experience, but if your load has any significant inductance or capacitance it will affect the damping factor and how it responds in each case.

there is a well written answer in a previous post, so I will refer you to it.

Ripple reduction with LC filter

since you want a formula, the dampening factor or quality factor are perfect let's assume we can reduce the whole circuit to series parameters. Everything is present, so R is all the resistance(load+filter) then C and L with the same line of thinking, of course your filter is not really connected in series, but the only change will be the ratio between the filter parameters and load parameters, they will still have an effect which is what I am trying to explain.

damp= \$\dfrac{R}{2}\sqrt{\dfrac{C}{L}}\$

different values of this, will yield different ripples and different responses, at the end you can evaluate the same thing with quality factor. In the linked post it is explained with figures and examples. Or you can investigate more.