To get Calibre to run on an ARM processor you would need to do a full port of Calibre and all its dependencies (around 100 at last count I think). This would be a non-trivial task although technically possible. I do not think that there is an existing binary distribution for the ARM processor.
However, having said that I would be very surprised if the QNAP is powerful enough or has the resources to run a Calibre setup. That was certainly the issue I found with my PowerPC based NAS system, and the
calibre2opds software is the current solution I use for providing online access to my library as it only requires a web server on the NAS.