What effect do slats have on descent rate?
If the slats would increase L/D, they would not be retracted in cruise.

TomMcW is right, any high lift device increases drag when compared to a polar point that is within the regular operating envelope of the clean wing. How much so can be answered when looking at old wind tunnel data published by Sighardt Hörner in his classic "Fluid Dynamic Drag":



Figure 6-20 from Fluid Dynamic Drag comparing different versions of the Fieseler Fi-156 "Storch" slat. Although it is not explicitly stated (and the original report in the Jahrbuch der deutschen Luftfahrt-Forschung of 1940 is not available online), it must be assumed that the lift coefficients of (a), (b) and (c) are similar. After all, Mr Hörner worked at Fieseler in Kassel and contributed to the aerodynamic design of the Fi-156, so he should have been intimately familiar with this airfoil.

Version (a) at the bottom is with a gapless slat and produces a drag coefficient of 0.015. Version (b) is with a gapped slat but blocked flow, and the drag coefficient shows a small increase to 0.018. Once the gap is opened (c), the drag coefficient jumps to 0.03. Note that at a higher angle of attack and lift coefficient (d), the drag coefficient is slightly reduced (0.028). But it is safe to assume that a deployed slat roughly doubles the airfoil drag.

If thrust and speed are not changed, deploying slats will increase sink speed. If I further assume that this descent is done at optimum L/D (zero-lift drag equals induced drag), then a doubling of the zero-lift drag of the wing will increase total drag by maybe 17%, details depending on the share the wing has in overall drag (I assume for the figure above that this share is ⅓).