seems the question is not only applying to c2 but for most developers over internet that uses node ... and i was trying to figure it out also this week.. till i found your post.. and seems is not possible
here is a topic for headless verison and seems that node.js already does it.. but not nodewebkit which is a different thing.
and also the phantom.js is doing same thing ... but im no plugin exporter developer.. so all this lays in your powers if you can develop a new nw.js like exporter plugin ... sounds easy but i know is not ...
ah.. and there is this repository also... git phantom nodewebkit
im just a noob dont beat me with rocks ...
however this thing may not be needed since you can install a GUI on linux ... and run ur app.. as i did (but was painfully long process)... another option... if u willing to put some server maintanance cash down... rent a windows server and its done(what im using now but its heavily expensive then a normal linux server 5x times more) ... but then just adding the ability to set window "show" to "false" in the manifest when exporting wold also do the trick.