From what I understand, no, you cannot. A possible options though is to set a Jinja variable if that pillar data isn't needed elsewhere, and use a Jinja include which can then see the Jinja variable.
Another option, though it requires multiple invocations, is to set a grain based on a pillar variable, and then in the next run reference the grain detail, using salt('config.get'), which will look at the minion's grains first and that variable would be set based on pillar data. It's not as dynamic, nor is it as secure, but it does work.
Ethan