Yes we can!
webOS is probably the most open platform in this sense since you can install apps from the official App Catalog as well as from Preware, which is the webOS answer to Cydia and will let you install what we call "patches" - little bits of code that are 'patched' over system code and can change pretty much everything about your system in terms of both features as well as look-and-feel - while also being much easier and legal to get.
Would you like different menu entries in your system menu? There's a patch for that. Would you like "Just Type" to say "Make it so" instead? Much to Jean-Luc's relief, there's a patch for that. Would you like everything to look different? There's a theme for that, and it's also found in Preware.
You simply type upupdowndownleftrightleftrightbastart (or the KONAMI CODE if you are, or have ever been, a gamer), enable "Developer Mode" and then install Preware using webOS quick install (a java program that runs on every windows, linux or mac PC - use the forum search function to find the newest version), and you're all set.
Takes about two minutes, is completely safe to do, and won't void your warranty in the slightest.
As for "sideloading", that's also possible - you can download any .ipk directly to your device (for example by going to Precentral's developer forums, where you'll always find .ipk files including apps, patches and themes, and downloading the files directly on your device) and install them using the "Internalz" file manager... although I'm not 100% sure if the paid App Catalog version of Internalz will do or whether you'll need the free Internalz Pro version from Preware. Yeah, that's webOS for you - the free stuff can in some cases be more powerful than the paid stuff.
In other words, all thinkable avenues of app / patch delivery are possible on webOS.
Hope this helps