No, it doesn't work like that.
Firstly, yes you can calibrate his work PC with your Spyder, as long as the Datacolor rules allow you to do so. And yes, of course anyone who is working in graphic design should be calibrated.
And yes, calibration will ensure that his website stuff will be correct.
But calibration alone won't guarantee his magazines print correctly. For that, he needs to ensure that he is working carefully with the correct CMYK profiles.
There is some partially relevant reading here and here. But to give more specific advice, I'll need to hear more about his CMYK workflow.