In the mentioned document, http://www.ietf.org/rfc/rfc4627.txt, it is stated that

The grammatical rules in this document are to be interpreted as described in [RFC4234].

RFC4234 describes ABNF (Augmented BNF), not EBNF. If you look through this document, you will find the following definition:

3.6.  Variable Repetition:  *Rule

   The operator "*" preceding an element indicates repetition.  The full
   form is:

         <a>*<b>element

   where <a> and <b> are optional decimal values, indicating at least
   <a> and at most <b> occurrences of the element.

   Default values are 0 and infinity so that *<element> allows any
   number, including zero; 1*<element> requires at least one;
   3*3<element> allows exactly 3 and 1*2<element> allows one or two.

So, notation

*( value-separator member )

is correct according to ABNF definition, and allows any number of repetitions, including zero.

"EBNF as lexer" is nonsensical. But the rest of your question can be interpreted as, "can I get a parser driven by an EBNF to produce an AST in JSON form?"

Sure.

Most parser generators accept (E)BNF and "parse". Most of them don't automatically produce an AST; they make the programmer define how each rule should generate tree nodes. Those won't work for your task.

Some do generate ASTs as data structures automatically using just the BNF and a source file: ANTLR4 (I think), and our DMS Software Reengineering Toolkit. Neither of these produce JSON directly, but in both cases it should be straighforward to write (once) a generic tree-walker that spits JSON.

DMS's BNF will handle any context-free grammar using just BNF rules. ANTLR4 handles most grammars but has restrictions on what you can write (e.g., certain kinds of left recursion are verboten), and requirements for you to add extra disambiguating information where the grammar isn't LL(1).

DMS will export XML directly. See this example.