Are 'effectually' and 'effectively' completely interchangable?

In the OED:

effectively, (adverb)—in such a manner as to achieve a desired result: make sure that resources are used effectively.

effectual, (adjective)—successful in producing a desired or intended result; derivatives: [...], effectually adverb, [...].

In Wiktionary:

effectually [...] Synonyms: completely, effectively.

In the Encyclopaedia Britannica I read:

Though the designs of the Frenchs against Jamaica were now effectually frustrated, the victory was not followed [...].

Further, in the Guardian I read:

Schools that had once been mixed were now effectually segregated.

So, I am confused if the above sentences would sound better as

• Though the designs of the Frenchs against Jamaica were now effectively frustrated, the victory was not followed [...]
• Schools had once been mixed were now effectively segregated.

Can you confirm whether effectually and effectively are completely interchangable or not?

Note: I read "'The team is moving around really effectively.' — Is this a correct use of effectively?", but there it does not answer my question.

Effectually is effectively archaic. Don't use it.

Note that OP's definitions evidence the fact that the two words are synonyms in the adverbial sense of "with efficacy", which normally implies purposefully and efficiently.

On the other hand, my own usage at the start of this answer has more the sense of "in effect, to all intents and purposes, in practice" (a meaning which also originally attached to effectually). But since most people probably won't be so familiar with the archaic form, presented with...

High dosage of morphine effectually/effectively ended his life.

...they might well tend to interpret effectually there as meaning the morphine was administered in order to give him a painless death, where effectively would often be seen as implying that death was more of an unfortunate/unforeseen/accidental consequence of the pain-killing treatment.

For all that, I would not recommend using effectually in any non-facetious circumstances.

The NOAD has the following notes about effective, effectual, efficacious, efficient:

All of these adjectives mean producing or capable of producing a result, but they are not interchangeable. Use effective when you want to describe something that produces a definite effect or result ("an effective speaker who was able to rally the crowd's support") and efficacious when it produces the desired effect or result ("an efficacious remedy that cured her almost immediately"). If something produces the desired effect or result in a decisive manner, use effectual ("an effectual recommendation that got him the job"), an adjective that is often employed when looking back after an event is over ("an effectual strategy that finally turned the tide in their favor"). Reserve the use of efficient for when you want to imply skill and economy of energy in producing the desired result ("so efficient in her management of the company that layoffs were not necessary"). When applied to people, efficient means capable or competent ("an efficient homemaker") and places less emphasis on the achievement of results and more on the skills involved.