Yes, the trial provides a fully working version with all features enabled, although only a small selection of templates in the Designs Gallery / Content Catalog are editable (the majority are thumbnails only, so you can see exactly the templates you will get when you purchase. The Content Catalog will show editable files in white and locked content in grey).
In Photo & Graphic Designer and Designer Pro 10 & 11 the PhotoLooks 2 plug-in is not included in the trial, in Designer Pro the Pan Studio panorama maker is also not included in the trial. In both cases these third party extras are delivered in the content pack after purchase. To install this pack, go to Help > Download Content Installer and follow the onscreen instructions.