Not directly… but if you want it badly, you can create a variable that has Replication setting set to RepNotify (it is a networking tool). Then, inside the OnRep_variableName function you can call the event to change specified material parameter.
Whenever you use “set” operation on this variable, the OnRep function will fire.
Note: increment/decrement will not fire this event, but you can set the value of variableName with the value of variableName 
True about C++, it would require additional function call, which is pointless, as OP wanted just to change the variable. Overhead? I’m 99% sure it won’t be the performance killer, it would had to be very specific project…
Is it possible to bind a variable in a class to a dynamic material instance parameter so that changing the variable automatically changes the material instance?
I have a pawn with a dynamic material instance that has color parameter, and I want that color to be reflected by a LinearColor variable stored in the pawn, similarly to how you can bind a function to a LinearColor attribute for a Text component in a Widget and then whenever you change the variable the text also changes its color automatically.
Or is the only way to do this to make an event fire off whenever I change the color variable and then manually set the dynamic instance parameter value whenever that event fires?
You’ll have to create an event, or alternatively, use a material animation curve that’s named the same as the material parameter.
This will only work for BP variables and has terrible and unnecessary overhead for this purpose.
True but it is still going through network-intended channels and the whole replication mechanism just to avoid a single function call.
Welp, event it is then!
This is a multiplayer game, so since I can’t bind the parameter to a variable I’m going to have to use a NetMulticast function anyway.