Can I use a kernel from a newer version of Ubuntu in an older version?

The Ubuntu HWE kernel packages are for exactly this purpose. It is also possible to get prepackaged kernels that are even newer than these.

The HWE kernels do not have any significant negative impacts. The biggest penalty for a non-distribution kernel is that it may not have gotten as much testing, and updates to it will occur outside of the distribution's update cycle, so you won't get updates unless you do it yourself. This could have security implications.