Yes, but export of images does not go beyond 1920x1080.
With respect to Ann's answer, there is a lot more to it.
One of the best parts of 4K is being able to pick very usable photos out of video footage. Until 4K picking frames from a video was hightly limited. The current dozen or so 4K capable consumer cameras from Sony and Panasonic shoot 30 full frames a second, kind of like continuous burst. Panasonic promotes it pretty hard and even has some in camera tools to capture frames. I've got prints to 13x19 that are clear and colorful.
In Premier Elements, there are two ways to capture still frames.
The Tools menu has Freeze Frame that will create a .BMP file, save it, insert it in the time line or both. From 4K footage it will be about an 8MP image of about 20MB. It is very quick, easy and useful.
With Export/Share > Comupter there is a choice for "Image". In PrE 13, the defaults don't go beyond 1920x1080, but the "Advaned" button offers more useful choices. You can set 3840x2160 to match the current consumer 4K format, minimize JPEG compression and elect to render at maximum bitdepth. The result will be an 8MP JPEG of about 6MB.
You are absolutely correct.
I was looking for the Advanced button but its now the custom button which I missed.