Let's start by looking at a pure "kick out the crab" technique, where we don't lower the upwind wingtip at all.
Even though we don't usually use the word "sideslip" when we talk about "kicking out the crab", we do in fact cause a sideslip when we press that downwind rudder pedal, even if we don't lower the upwind wing.
When you kick out the crab you force the aircraft to slip (or we could say skid) sideways through the air. A yaw string on the front of the windscreen would blow sideways, in the downwind direction (if there were no propwash). This is not an efficient way to fly. Initially, the slip angle is fully as large as the crab angle you just kicked out. As the flight path starts to curve (because you didn't lower one wing to stabilize the situation)-- i.e. as the aircraft starts to "accumulate drift" (which in reality is actually a turn -- a curve in the flight path--a rudder-commanded "flat turn" or skidding turn)-- things change, but that's the initial situation. So the more crab you kick out, the more the aircraft is forced to fly sideways.
For any given approach airspeed and any given crosswind component, as headwind increases, so will the required crab angle, so when you "kick out the crab", you'll have more sideways flow over the aircraft, and the sink rate will increase. You may also notice an increased tendency to roll toward the downwind wingtip, due to slip-roll coupling.
It may help clarify things to understand that "kick" is a little bit of a misnomer. After the "kick", if touchdown is delayed, to keep the plane aligned with the runway, you have to keep HOLDING some rudder pressure. If you released it, the plane would tend to swing back into line with the original flight path-- the nose would swing back toward the original heading. After a few seconds though, the plane has "accumulated enough drift"-- i.e. the flight path has TURNED or curved enough-- that the aircraft heading will be aligned with the runway even with no rudder pressure. You do not want to be in this situation, because it means you have TURNED your flight path through the airmass so much that it is fully aligned with the runway heading, and you have TURNED your ground track toward the downwind edge of the runway. You'll soon be in the weeds. That's the trouble with the pure "kick out the crab" technique-- if touchdown is delayed, you have a problem.
Up till now this answer addressed a pure "kick out the crab" technique, but you did in fact mention sideslip in your question. If at the same time you give the downwind rudder input, you also lower the upwind wing, you'll have the same initial slip angle as described above, and a headwind will affect the required slip angle-- and the resulting sink rate-- in the same way as described above. But if you lower the upwind wing to stop the rudder-commanded turn, then the situation will be stabilized and you'll see that same slip angle (and that same sink rate) all the way to the ground -- assuming of course that the crosswind component and the headwind component are both constant all the way to the ground, which may very well not be true in reality.
(We're ignoring here the effect that banking has on sink rate, which is real but but probably quite a bit smaller than the effect of flying sideways through the air (slipping/skidding) due to the rudder deflection.)
At any rate, whichever technique you use, for a given crosswind component and a given approach speed, more headwind = a larger crosswind component = a larger slip angle = a higher sink rate.
If you are crabbing along on final approach with NO wing-down correction, and you haven't yet "kicked out" any of the crab angle, then the plane doesn't "know" anything about the wind at all, for a given power setting and angle-of-attack. It's only after you "kick out the crab", or after you initiate a wing-down cross-controlled correction, that the strength of the headwind matters, because of the way you must adjust your control inputs to match the required slip angle, which is affected by the strength of the headwind.
In actual practice, with the cross-controlled wing-down technique, it seems to work well to imagine that the lowered upwind wing is somehow "opposing the wind" and "stopping the downwind drift", while the rudder is controlling the heading. The real truth though is that what the lowered upwind wing is really doing, is stopping the rudder-commanded flat (skidding) turn that would otherwise take place if we "kicked out the crab" and didn't touch down immediately after.
