Both Premiere Elements 12 and 13 have project presets for the video with the resolution of 3840 x 2160 (a 4K resolution) under NTSC only. It also offers
export of the 3840 x 2160 resolution under Publish+Share/Computer/XAVC-S. There is no burn to Blu-ray with any 4K resolution.
Remember, that 4K is a resolution. And, the video codec from manufacturer to manufacturer can vary which impacts the question. The generalization is that
H.264.mp4 4K video is supported by Premiere Elements 12 and 13.
Project Presets, please see NTSC/AVCHD/QFHD choices
Export Opportunity to .mp4 file - please see Publish+Share/Computer/XAVC-S and its presets.
Any questions or need clarification on any of the above, please let us know.