The answer is yes, it exist non-synaptic plasticity as you can read "[Non-synaptic neuronal mechanisms of learning and memory in gastropod molluscs][1]" by Benjamin et al. and "[Compartmentalization of Non-Synaptic Plasticity 
in Neurons at the Subcellular Level][2]" by Nikitin and Balaban.

But effect of hormones such as cortisol may also have an effect. 

Non-synaptic mechanism of regulation, and plasticity has very important role in the brain and is ability to learn in many aspect and at different scale. 

A single cell can suffer internal modification that will modify eletrophysiological properties. 

variations of concentration of elements in the CSF also have an effect. 

Glia also has an important role... 

So, brain is very complex system with lot of interdependent mechanisms of adaptation, regulation and plasticity. Synapse is just one aspect of it. 


  [1]: https://www.researchgate.net/publication/5341470_Non-synaptic_neuronal_mechanisms_of_learning_and_memory_in_gastropod_molluscs
  [2]: https://link.springer.com/content/pdf/10.1007%2Fs11055-014-9975-5.pdf