The question is pretty short, but I've been thinking about it quite some time: Are terminal symbols that are not in the defined alphabet still valid?
No. The grammar is defined like this:
G = (V,SIGMA, R, S) where V is your set of variables (non-terminals) and SIGMA is your alphabet (terminals). All the symbols you are allowed to use in the substitution of a rule are the union of V and SIGMA. If you simply cannot use a symbol out of that set, since it does not exists in the context of your grammar.