Your POM defines how a project is built. If you change it, typically you are changing something about how the projects gets built. Therefore it's only logical that you would rebuild the project (recompile) to reflect those changes.
An IDE is no substitute for an Intelligent Developer.
I guess it depends on the change that you made and what your end goal is.
Did you add a dependency? Then maybe. I assume that the project built and the tests ran without it, so adding it might not have that much of an impact. But if you are packing your project using the asembly plugin and you noted that that dependency was missing, then yes re-run the build so that it gets included in the package.
Did you change the artifact's description? Then only if you plan to regenerate the site would you need to build again.
Did you add or change a plugin? Then yes because you have changed how the project gets built.
Did you change the version number. Then maybe. If other projects are already referencing yoru artifact by the new number then yes you must rebuild. If not, then you don't have to.