In most cases the answer is no, but there is one exception. Info from the Oxford Advanced Learner's Dictionary: take something <-> up 8) to return to an earlier subject or situation in order to continue it pick up on something 2) return to a point that has already been mentioned or discussed Note that use #8 of take up something is the same as use #2 of pick up on something.

I see you've added examples. Those suit the dictionary entries I posted about.