The phrase you quote in your title is a metaphor meaning 'use Voltaire's words to articulate or defend my position' complete with an allusion, an explicit reference to Voltaire.
Later comes another allusion, much more indirect, to this quote from Voltaire: "I may not agree with what you have to say, but I will defend to the death your right to say it."
The initial metaphor, as is later revealed, is wrapped in a proslepsis, a form of paralipsis, "stating and drawing attention to something in the very act of pretending to pass it over".
Altogether, then, what you've cited in your question is an anamnesis, a referral to authority (usually by allusion). In this case, the authority referred to is Voltaire, and specifically the quote from Voltaire.
For definitions of all the terms I've italicized, see The Forest of Rhetoric. A search feature is available, central top. Many more rhetorical elements are exampled in the quote you've provided.
So, your final questions:
The quote from Voltaire is related to the view expressed rather remotely, because what the view expressed by the quote becomes has only a remote connection with what Voltaire actually said.
The language used, more properly the way the language is used, is highly figurative. I've mentioned some (only some) of the figures used in italics, above.
