Mathematica already notifies you that the output is special:

Also:
??Base
gives:

notice that it says print...
I'm not sure what else you want them do? Your expression Baseform[...] - 400 is equivalent to "Hello" - 400, it doesn't make much sense...
Of course you could add a rule:
Unprotect[Plus]
Plus[BaseForm[a_, b_], c_] := a + c
BaseForm[100,16]+12
112
But be VERY careful changing the definition of Plus! It is protected for a reason!