Yes but it is not very elegant.
"INPUTPARAM" is the name of your mask variable. You have to follow that to get the name of the Simulink.Parameter object, e.g. "MyParam". Then you have to evaluate "MyParam" in base workspace or data dictionary to get a copy of the object, then you can have the "unit" property value.
One trick is to use Simulink.data.evalinGlobal(). It works for both base workspace and Simulink Data Dictionary so you don't have to detect it first.
For Simulink Data Dictionary, there is supposed to be a few API that you can use to access the property value more elegantly. But at the end you still have to make a copy of the object. Since R2018b, I have requested the Mathworks to provide/develop API to access object property value directly. I have not checked the recent versions.