Delighted to make your acquaintance, Mr Troglodyte, and the simple answer is No. Words like "unbeknownst" are relics of a much older style of English (when the grammar was closer to its sister language, German). Meeting words like this is similar to finding fossils on the beach. Accept these archaic-looking words if you happen to come across them, but don't try to draw any conclusions or see any patterns.

In American English at least, unbeknownst is not that uncommon. "be + root word" usually means roughly "to turn into (root word)" To befriend someone means to turn someone into a friend. To bewitch someone means to turn them into someone under a spell. The st suffix is a relic of German's influence on English and has no meaning. Amongst and among mean the same thing, along with amid and amidst. The only word I can think of where it makes a difference is against and again.

In my experience in US English "unbeknownst" is not common as a "straightforward" usage. It would be understood, but it would be usually used humorously, as an intentionally outdated expression. It sounds like the sort of thing you might see in a silent-movie caption: "Unbeknownst to the hero, the villain was treacherously lurking in wait for him." I would not practice trying to "apply this pattern" to other words; it's not a useful pattern.

so true @su.ku. however for this particular fossil, if one uses it, it will still be understood. for example: Unbeknownst to me, my father paid my rent directly to the landlord.