Bonjour Christophe,
Yes it is possible to calibrate and registrate and stack your spectra in PI. Calibration (bias dark and removal of hot pixels and cosmics) is done just as for standard images. For registration, Pi can work with the zero order images of the stars (assuming your working on spectra obtained with a star analyzer) but I could not find a way to register the spectra only. Stacking can be done as usual. And yes, you can batch crop your fits images to reduce the size of the images and work only on the spectrum and the zero order star image (and even registrate the spectra while doing so).
Just make sure to keep the spectra images linear, with no treatment at all, before analysis in e.g. VSpec.
Hope this helps,
Jean-Phi / apricot