No, not really.
It's got a great strength to weight ratio, but it might be better to say they reduced the effective weight while retaining most of the strength of the material.
The stuff needed for the cable of a tethered satellite needs a lot more than just a great weight to strength ratio, it needs a certain level of strength and resilience.
Look at it this way, if you had a steel component that weighed 1,000lbs and could hold up 20,000lbs and you replaced it with this type of similar to aerogel lattice type steel component, you are looking at a tiny weight (probably) less than 3 lbs, and it could still hold up around 20,000lbs. Of course, if the project needed a component that size that was able to hold up 50,000lbs, neither one would be feasible.
Some people might suggest that you could just make it bigger, but that's often not a feasible idea, even if it is lighter than the usual materials. For one example is why skyscrapers are not made of brick. It doesn't matter how wide your walls of brick would be, after a certain point, the weight of the bricks would crush the lower ones, and then the whole building collapses. The steel reinforced concrete we use can sustain much larger loads, and so is used for tall and heavy projects instead of bricks. Of course tethered satellite has to withstand much greater stresses, whether it's crushing down, pulling up, or swaying to the side. That's why super light but otherwise more conventional materials won't work.