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These failures can not only motivate us to find a successful way to accomplish our goal but also help us to grow in wisdom and in spirit.
I learned that "not only A but also B" and "B as well as A" are interchangeable. But I wonder if I can apply this to the above sentence.
Yes, of course you can:
These failures can not only motivate us to find a successful way to accomplish our goal but also help us to grow in wisdom and in spirit.
Which becomes:
These failures can help us to grow in wisdom and in spirit as well as motivate us to find a successful way to accomplish our goal.
Both of those sentences are grammatical. There may be a subtle difference in meaning, but the rule you give is certainly applicable.
In terms of strict declarative meaning, "not only A but also B" means "B as well as A" or "A as well as B", or "A and B". However, it is different in nuance.
For not only ... but also, the first statement, A, is implied to be one that is obvious, that people will easily realise, perhaps without being told. It might even be something they have already been told explicitly. B, on the other hand, is suggested to be a less obvious thing, a thing you would not expect them to know or work out - at least not as easily.
