No Chris - science cannot legitimately speak about “undetermined” at all - how on earth could scientific methodology ever show that? It can only speak about “random” strictly in the sense of "cause unknown ".
As soon as someone - scientist or not, Christian or not - says “undetermined”, they’re doing metaphysics, not science - and their metaphysics at that point is unquestionably Epicurean.
Expansion: as far as legitimate science itself goes, there is no known or proposed mechanism for indeterminate change within nature anyway. I guess the sole exception - quantum changes - would have to be seen as either having an efficient cause outside nature, or in some unsuspected part of nature, or (speculatively) as uncaused in full Epicurean dress uniform. But few people are actually considering quantum causation in the matters under consideration in life studies.
CHANCE IS NOT A CAUSE - it is an expression of ignorance of cause.
Footnote: To speak of the same event a both undetermined and governed is a flat logical contradiction. In other words it’s incoherent.