A delicate situation, indeed. I have joined parties like this where the party leader was only chatting in text, while I am typically very vocal. But, never to the point of disregarding party chat, or trying to usurp the party leader.
In fact, I will often say in voice chat, "We could do it this way, but ultimately, it's up to the party leader. What say you, party leader?" to defer leadership back to the proper place.
Still - I feel that leading groups is much much easier done (not to mention following a party leader) when the party leader uses his/her mic.