Not exactly, no. But there a few workarounds.
You can quickly copy the materials from the active object to all selected objects with ⎈ CtrlL> Materials.
Combining that with groups, you can "store" selections of objects for later. Group the selected objects together with ⎈ CtrlG, then update the materials of the group by activating the object with the updated materials and pressing ⇧ ShiftG (to reselect the group) then ⎈ CtrlL> Materials.
I know you specifically asked about switching materials and not about altering a single material. However, if you relax that constraint a bit you can use node groups to achieve this. Put the entirety of your material in a node group (A to select all nodes, then ⎈ CtrlG), and voila:
Note that in this example, the objects have separate materials: "Material A" and "Material B". They could instead share the same material, or have multiple materials each, some shared and some not. The link is through the node group.