In terms of clause analysis, does this constitute a complex sentence?

grammar clauses

In the words of CGEL (§ 10.1 p. 719), a complex sentence is recognized by the fact that "one or more of its elements is realized as a subordinate clause".
Thus, the object "how their tiny bodies would cope with what they had to carry" being a subordinate, this sentence is complex; that is all there is to it.

"with what they had to carry" is a subordinate clause of the subordinate/ superordinate clause "how their tiny bodies would cope with what they had to carry".

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