Howdy, I game on an ultra portable with an eGPU. I'm currently running a Gen 1 Thinkpad X1 Nano, specs are the following:
i7-1160g7
16Gb RAM
2160x1350 Resolution
I then have the Razer Core X with 6650 XT running through Thunderbolt 3 (most eGPU enclosures run on older Thunderbolt 3. There's some newer stuff with Oculink, but you'll be spending more money for that setup.
Anyway, there's some caveats and gotcha's with this setup: Thunderbolt 3 can only run at a maximum of 40Gbps via PCiE x4, that's just how it is, so you're going to be losing some performance over that, nothing to be done there. As well, if you're planning on gaming on the laptop monitor itself, expect to lose even more performance, as now your PC is sending the data out to the eGPU, data is getting sent back, processed by the CPU again and then finally put up on your laptop display. You'll actually suffer considerably less performance loss by plugging in an external monitor to the eGPU.
Another caveat: The higher resolution you play at, the better games will perform. I can't explain in depth here because I'm not that smart, but due to the way eGPU's work, you're actually suffering more performance loss at lower resolutions versus high, I believe this has to do with how much the CPU has to work to send data to the card, but don't quote me on that.
All that said, I don't do that, because I prefer to move my laptop around the house and then go plug in to my eGPU next to my couch for the extra performance. It also allows a little more mobility in that I can move my eGPU around the house, though I honestly don't do that as it's pretty much the size and weight of a small PC at 14lbs.
Now again, all that said: Don't expect miracles. An Ultraportable is still a pretty low power chip, mine is a grand total of 15w, so I often find that my CPU usage is pegged while the GPU is being underultilized. I suspect I'd see better performance if I had a computer with higher wattage and clocks, but I don't have anyway to confirm that right now and of course, you're then making the tradeoff of having something less portable.
So for me, it does give a considerable performance boost and I'm able to play a lot of things that I couldn't normally run on the integrated graphics. Aliens: Dark Descent works lovely at all "Epic" settings, easily running at 60FPS most of the time, but dropping here and there to mid-40s. Kingdom Come: Deliverance, Mechwarrior: Clans, GTA V all run pretty good, the former two being around 30FPS and GTA V being anywhere from 30 on the low up to 60 FPS. I just played through all of Dishonored 2 at around 45-60FPS. As you can tell from this paragraph: Performance is kind of all over the place. Again, don't expect miracles. some games work wonderfully others hit and miss and some not at all, basically, it's not foolproof.
It's also worth considering that most ultraportables are not upgradable, generally. I did upgrade my NVMe in my Nano, but RAM is soldered, so you're stuck with whatever you buy.
Would I do it all over again? I'm not sure. I love my Nano for it's ultraportability, but I also don't really travel much and even when I do, I don't use my laptop that much. I'd love to have something in the size with even a basic dedicated graphics card, because it would mean that when I move about my house, I'd have more options for stuff to play without needing to also haul the eGPU around the house. It also has all those other caveats that come along with it, enough to the point that I've been mulling over buying something more powerful, both for a dedicated GPU and also to see if my eGPU setup would perform better with a more powerful system.
Also, while I like my 6650XT, it performs well and was pretty cheap ($190), I think I'd go with Nvidia next time. I've run into a few issues where compatibility with AMD and the eGPU is just a little bit wonky; no issues on my desktop with an AMD card, but in an eGPU setup, I've run into issues, especially with older games (Dishonored 2 and Deus Ex: Human Revolution). YMMV, it's a neat setup and I do really enjoy being able to do something that seems subversive (heavy gaming on an ultraportable), but it comes with all the caveats and issues listed.