Well, I have always taken this line to describe his composition process, so sure, I'd say it applies to "Birches." He took an initial spark of wonder and reworked it into something meaningful. That's a kind of wisdom.
Now, does it apply for the reader? Only moderately, because, to be frank, I find only moderate wisdom in the poem, and because the poem's delight is not located only at the beginning, but rather throughout the poem.
The poem's delight comes from its imagery: their clarity, vividness, how fitting they are. That is true at the beginning and at the end.
As for wisdom, it is true enough that " One could do worse than be a swinger of birches." I agree with it. One could do worse—but is that enough to qualify as wisdom?