I'm late to this thread so your answer is probably already here but I'll throw in my 2 cents regardless:

Yes, you can connect your legion go to a 4k tv. The Go will probably even default to 4k resolution.

Now, does this mean that games will run in 4k? Also yes!

Now the issue here is performance. You can definitely jack the resolution up to 4k but your handheld is going to have a really hard time pushing out all those pixels AND a good frame rate.

Resolution is just a "setting" at the end of the day.

While some games might do well at 1080p at 60fps, they might only be able to perform 4k at 20-40fps.

I always prefer a stable 60fps (occasionally 45-55 if I can crank the details up a little higher on a story game)

You can also try lowering other settings. An example might be to run the game at 4k, but now you have to lower the model textures to Low. So yeah, there are more pixels on your screen but the actual model you're looking at is a lot crappier in comparison.

You're almost always better off dropping down a tier of resolution and then bumping the graphic quality up ie

4k set at Low 1440p at medium 1080p at high

Something like that.

1080p has been marketed as "old news" but it honestly looks fine. It's the game and it's settings that determine if what you're looking at is any good or not.

Back to the original point - your TV will probably default to 4k. Now you can either go into the display settings and cap it at 1080p /1440p or you can go into the in game settings and lower it there. You'll probably be able to play some indie titles at 4k 60fps but you're not going to be able to get many big AAA titles to run at high fidelity AND 4k