There is a way to perform some amount of kernel upgrade testing inside a container. Even though containers don’t run their own kernels, you can still install kernel packages inside containers, and upgrade them, so you can check that the package upgrades are correct.
However there is no way to verify that a kernel boots inside a container. To do that, you need some sort of VM, either emulated or virtualised (e.g. Qemu with or without KVM). You can also drive that from inside a container if you want, and if the host is set up to allow it. See RancherVM for an extreme example (on Kubernetes).