I would like to build labview applications to be run on a (headless) single board computer, or possibly a windows CE device like an IPAQ handheld computer. The interface would involve some type of simplified keypad, with just a few keys, and a small display.
Not yet. It's pretty common knowledge that NI has been working on porting LabVIEW to Palm and/or CE for some time. They even had a demo last August at NI Week. When it's going to be released is anybody's guess however.