Depending on what you want to do, this might be already offered. If you want to run a web tool on the same server then you should be able to import the toolbox and run it. If you want to schedule a tool in a local tbx this should also work. If you can share more details we'll be able to respond.
if I use a script that calls a local toolbox (.tbx), which in turn runs a .fmw file (FME workspace), can I execute everything from my notebook machine (as the client), or does it have to be run from the server?
As far as I know, provided the ArcGIS Server machine hosting the notebook has Data Interoperability installed and licensed it should be available to the advanced runtime. Best to check with arcpy.CheckExtension('DataInteroperability') before you invest a bunch of time in it - please let this thread know!
