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?
I think it definitely applies. :)
To 'begin in delight' and 'end in wisdom' need not be restricted to the flow of the poem, nor the creative process of the author, although both of these may fit. In most poems, Birches included, I think these apply more to the experience of the reader.
The delight felt by the reader may be amazement at the way the poem skillfully paints a picture or elicits emotion, or even just the way it manipulates language for effect. "Fire and Ice" is a good example of this, where both rhyme and rhythm make us smile and think "Brilliant!" Birches is certainly abundant in lush and clever imagery and loaded with nostalgiac feelings of wistfulness, joy and sadness for what is lost to the passage of time. Most who appreciate poetry would find it delightful.
But it would be not be complete if that's all there was. A good poem (and perhaps most do not qualify) also reveals depth of thought. It does not need to convey some moral direction or profound statement of truth in order to 'end in wisdom.' Rather, if it simply succeeds in causing the reader to reflect on the connections between things, the causes and effects, the motives and meanings ... then it is sharing wisdom. In this repsect, Birches is rich:
So was I once myself a swinger of birches.
And so I dream of going back to be.
It's when I'm weary of considerations,
And life is too much like a pathless wood
I'd like to get away from earth awhile
And then come back to it and begin over.
Doesn't this make you stop and ponder what you've left behind, the mistakes you regret, and what you can do now so that you don't later wish to leave the planet and start all over?
Yes, I would say that for me, this poem indeed 'ended in wisdom.'