In ArcMap I can set a search Tolerance when loading incidents and facilities as points along a network for performing a closest facility analysis. Can this be done when running task over ArcServer with JavaScript?
It all depend, which task you are using and how you are implementing. If you use QueryTask, you may not achieve it without providing a buffered geometry. Analysis widget is a whole other thing. check out Working with Analysis Widgets | Guide | ArcGIS API for JavaScript and see what works for you.
