After I upgrade the kernel with ukuu, will Ubuntu be able to update the kernel without using ukuu? I wish to know if we have to continue to use ukuu to update kernels upgraded by ukuu, or if Ubuntu can do that without ukuu.
No, You'll need to keep running ukuu to stay updated.
But I'd question whether you really want a mainline Kernel from ukuu at all.
ukuu downloads packaged mainline kernels from kernel.ubuntu.com. This isn't a real PPA or repository so Apt (what manages your other updates) will never directly interface with it. Only uuku (or manually downloading and installing) will keep this updated.
Ubuntu will keep updating the version of the Kernel that shipped with your install, but the likely bigger version number of the ukuu-installed Kernel will displace the it when your bootloader goes to pick. This is just how the grub assembly scripting works by default.
I should add that mainline kernels aren't all that either. Newer isn't always better. They're raw kernel.org builds with minimal build and packaging patches. People won't backport security patches for you. People won't apply the performance and stability patches for you. They're really just there for testing and working around really new hardware issues.