There will definitely be a bottleneck but that
always happens because no two components will ever perform
exactly the same. What's important is whether or not the combination of X-CPU and Y-GPU will still give you the performance that you want.
Modern video cards have advanced in speed to the point that even the "mighty" i9-10900K will bottleneck the "lowly" RX 6600. Trust me, how insane that sounds is not lost on me and I never would've believed it until I saw it demonstrated:
The truth is that if the i9-10900K can bottleneck an RX 6600, there's absolutely no question that the i9-11900K will bottleneck the RTX 4080, a card that is literally
three times as fast as the RX 6600 because there's no way that the i9-11900K is three times as fast as the i9-10900K. Intel's performance increases at that time were... well, everything was a glorified Skylake CPU at the time so the performance increases over the generations weren't exactly staggering (to say the least).
You'll get a serious bottleneck but that just means that you'll be gaming at your CPU's top speed, not your GPU's top speed. The thing is, I don't think that you're going to be unhappy with the gaming speed of your CPU. The i9-11900K is a fantastic gaming CPU and while it will hold the RTX 4080 back quite a bit, I don't believe that it's going to make your gaming noticeably worse and if/when you upgrade to a top-end gaming CPU like an R7-7800X3D, you'll see huge gains.
Also remember, this is at 1080p, a resolution that nobody buys an RTX 4080 to play at. You can nullify CPU bottlenecks by increasing the resolution so you should be more than fine.