Can "whence" be used to imply causation?

Merriam-Webster gives the definition and example:

whence ...

b: by reason of which fact [, from which]

• [N]othing broke—whence I infer that my bones are not yet chalky.

• Aristotle is a human, whence I/we can deduce that Aristotle is mortal.

follows this form, and 'I/we can deduce that' has been deleted in the example you give.

Collins seems to license the 'which mandates [entails, means] that' (or 'which gives rise to') (causative) sense, but does not give an example:

whence [conjunction] ...

3. from which place, source, or cause

YourDictionary gives the odd example:

• For the world as a whole, however, he postulated a beginning in time (whence his use of the word creation), and further supposed that the impulse of organization which was conveyed to chaotic matter by the Creator issued from a central point in the infinite space spreading gradually outwards.
• Let 0 be the angle which the standard magnet M makes with the meridian, then M'/R = sin 0, and M/R = cos 0, whence M' = M tan 0.

I've seen this deletion (and 'hence') reasonably frequently in books on trigonometry and numerical algebra, and on geometry. But I'd agree that it's uncommon nowadays, and at least bordering on the archaic. I'd avoid using it in non-technical registers.