Is a regular grammar valid if it only contains production rules that have nonterminals in the right operand?
Back to the definition. According to Wikipedia, a context-free grammar $G$ is a 4-tuple $(V, \Sigma, R, S)$. In this case, $G = (V, \Sigma, R, S)$ can be defined as


$V$, nonterminals, is $\{S\}$,
$\Sigma$, terminals, is $\{a\}$,
$R$, production rules, is $\{ S \mapsto Sa \}$, and
$S$ is the start symbol and an element of $V$.


So this is a context-free grammar although the language recognized by $G$ is empty as you noticed.

You can also verify whether this is a regular CFG by going back to the definition.