I would not recommend.
They may feel more "cushiony" or "bouncy" but in reality they displace the proportions of the heel.
If you put that on, you're adding height to the sole of the heel but
nothing to the stiletto to match the added height.
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Adding on that sole protector may not feel like much. Maybe 1-3 mm of thickness, but believe me, it makes a difference in balance and weight displacement. I once put on a sole protector that was thicker and it totally threw off my walking and make it very uncomfortable. And I am a person who loves high heels and has a relatively high pain tolerance.
Also, because that sole protector does not cover the entire sole, you will inevitably kick it off if it gets caught on something like an edge of a curb or stair. Unless, of course, you perfectly put your foot down perpendicular to the ground you are walking on. If you make more of a sliding motion when you walk then that horizontal part of the force being applied will start pushing and peeling back on the sole protector.
If anything, buy an insole to put inside the heel. Or if you prefer a platform, because they can make it easier for people to walk in (not for me though), then maybe try on a pair with a platform to see if it works better.
I enjoy CL but I only buy Iriza's. They have a narrow stiletto but they are very comfortable for me.