I agree with the 'easier discussion' aspect of a whiteboard, but I feel that any whiteboard test should therefore be asking for pseudocode and explicitly disregarding the pedantic reality of syntax.
Yes. I do think there's a benefit in having a reference language--just don't be pedantic. For example, certain design patterns might be needed for C++ that are built into a language like Python. Knowing which libraries the candidate (or the company) leans on is a good topic to discuss. Pure pseudocode might be too generic to suss this out. It depends what you're evaluating them for. There's little to no value in testing them on things like mismatching parens or typos in variable names (I've heard stories about people getting called out on those things using a whiteboard).