This is a bit confusing to analyze because there are two hard variables and two soft variables. The resulting answer is going to be stupid.
The hard variables are the spring rate and the suspension geometry. The soft variables are what you would choose for static sag and what you feel comfortable with for a seat height.
Imagine a 100lb bag of cement, a brick, and an 8ft 2x4. In your mind, rig up the three things so that the 2x4 is resting under the bag of cement and on top of the brick such that there is 2 feet of distance between the center of the bag and the center of the brick, leaving 6 feet of 2x4 available as a lever to lift the bag of cement. This will represent the suspension geometry's lever on the spring (the brick and 2x4) and the spring itself (the bag of cement).
If you install lowering links what you are doing is moving the brick so that the 2 feet of distance becomes 1 1/2 feet and the 6 feet becomes 6 1/2 feet. That makes it easier to lift the bag of cement; it requires less force. However, the bag gets lifted less for a given amount of movement at the end of the lever. This represents the reduced amount of travel due to increased sag.
The effect is that if, when you previously sat down on your bike, it sagged 2 inches it is now going to sag something a bit more than 2 inches. Let's say it sags 3 inches. That lowers the seat height by an inch. Cool; the lowering links lowered the bike! Of course, that same effect is going to come into play when you hit a bump and exert more force on the spring. The bike will tend to bottom out easier. That's the disadvantage of lowering links.
Now, let's go back and put another half-bag of cement on to of the existing one. This represents installing a stiffer spring. The lever is still at 1 1/2 feet and 6 1/2 feet, but you've made the cement load (the spring) heavier, so it is going to take more force exerted on the lever to lift it.
Do you see where this is going? You spent $20 on a pair of links and a $100 on a spring and you may wind up just about right back where you started. Exactly where you'll wind up would require an analysis of all the levers in the suspension and knowledge of the spring rate of the OEM and the replacement shock.
The stupid answer is "Try it and find out".
The smart answer is to install either lowering links or a softer spring and live with the results, or spend the money on a better and more customizable shock such as the Cogent Moab to get what you really want, which is a lowered bike with a given spring rate.
Now, here is a semi-smart answer. You have a Gen 1. The Gen 2 suspension pivot reduces the travel somewhat and also lowers the bike. I have used this phenomenon to good effect to raise my Gen 2 by installing a Gen 1 pivot. You could go the opposite way and try installing a Gen 2 pivot. This here is what I'm talking about
and that, at ~$40, is the usual going rate for the pivot, bolts, and links.
It might be worth a try.