Is the intention not to rely on or work with a non-Muslim, when saying, "Allah alone is sufficient for me, and how excellent an agent is He," considered binding, taking into account the potential need for that?

There is no objection to working or studying with a non-Muslim, so long as it does not lead to committing something forbidden by Islamic law. Reliance [upon Allah] (Tawakkul) is an act of the heart that depends on the sincerity of trust in Allah while taking the necessary means. Taking permissible means does not contradict reliance [upon Allah]; rather, it completes it.