You are correct that the Elgato does video encoding. And that if you use your GPU it's putting a little bit of extra load on the GPU. But it's negligible since the video encoding is a separate part of the chip. Maybe you'll lose a percentage of FPS due to power usage snd bandwidth, but honestly the same is probably true for the CPU load caused by USB bandwidth.

I thought that passing everything through it would allow the USB to feed/write the video stream without any other processing

Unfortunately no. It captures the signal and turns it into something that the computer can digest, but the signal isn't something that just proxies straight through to twitch. OBS is always going to do some re-rendering.

A few tips:

If you open OBS settings, there is a "Output" section. You can change the output mode to "Advanced", and then select a "Video Encoder" ... this is where you would find NVENC (there might be a way to do it in the simple output mode too, but I dont have an nvidia GPU to confirm.

You'll most likely want to change the Output resolution on the "Video" section of the settings down to 1280x720. Twitch limits your bandwidth anyway, and people tend to find that 1080p at low bandwidth doesn't look any better than 720p at the same bandwidth (less compression artifacts because it doesnt have to compress as much, if at all)

Twitch has an option for bandwidth tests (or at least used to). This will make their servers accept the stream, but you don't actually go live on the site. You can use this to see how your computer handles the streaming. On the main OBS dashboard, you'll see a 30.00 / 30.00 FPS in the bottom right corner (or whatever your resolution you've selected). There's also a CPU meter down there.

In the Docks menu there's also a Stats dock. It will tell you how many Frames are missed due to rendering or encoding lag. If you have 0 missed frames, then your PC is handling the encoding just fine. It will also list how many dropped frames due to NETWORK you've had. This would indicate that there is a problem between you and Twitch/Youtube on the internet. Your computer is rendering the frames just fine, but Twitch isn't receiving them.

Use the stats dashboard to figure out where you are losing frames and then fix that (if its rendering/encoding, then its NVENC or your CPU struggling. if its Network, then its your ISP struggling). And if you aren't losing frames, then you have nothing to worry about. This dashboard will also show you CPU and memory usage, but realistically, if youre using a 3080 with nvenc, those usages will probably be very low.

They can. But Elgato also makes a "Camlink" in addition to the "HD60" series. And the Camlink dongles create a UVC device, which can be used as a webcam with no further tweaking necessary. Using a full desktop capture card for a webcam is slightly overkill, but absolutely works.