Do you need a few years in yeshiva in order to absorb the style, or just to acquire knowledge pure and simple?

It is much more than either of those. It is a whole mode of relating, knowledge, types of analysis, and contexts. Were I not afraid to say it, I would say: “Torah mentality.”
About this, the national poet already wrote (I tried to emphasize the important line in bold, but it didn’t work. See the markers that appeared instead):

If you desire to know the wellspring

From which your brothers, those who were put to death,

In days of evil drew such strength, such greatness of soul,

Going forth joyfully to meet death, stretching out their necks

To every sharpened knife, to every lifted axe,

To mount the stake, to leap into the flames,

And with “One” to die the death of the holy—

If you desire to know the wellspring

From which your brothers, the oppressed,

Between the straits of Sheol and the distresses of the pit, among scorpions,

Drew divine consolations, confidence, power, patience,

And iron strength to bear every burden of toil, shoulders

Bent to endure a life of filth and contempt, to endure

Without end, without limit, without outcome—

If you would see the bosom into which were poured

All the tears of your people, its heart, its soul, and its bitterness—

The place where its cries were spilled out like water,

Cries that shook the belly of the nethermost Sheol,

Sighs at whose terror even Satan shuddered,

Lamentation that shattered rock, but not the hard heart of the enemy,

Bolder than rock, harder than Satan—

If you desire to know the fortress

To whose summit your fathers escaped with the burden of their souls,

Their Torah, their holy of holies—and saved them;

If you would know the hiding place in which was preserved—

And in the essence of its purity—the mighty spirit of your people,

Which even when sated with a life of disgrace, spittle, and shame,

In its old age did not betray the desire of its youth—

If you would know the compassionate mother,

The old mother, loving and faithful,

Who with great mercy gathered the tears of her lost son,

And with great pity made firm all his steps,

And whenever he returned ashamed, weary and worn,

Under the shade of her roof she wiped away his tears,

Covered him in the shadow of her wings, lulled him to sleep upon her knees—

Alas, afflicted brother! If you do not know all these—

Turn to the study hall, old and antiquated,

On the long, desolate nights of Tevet,

On the burning, blazing days of Tammuz,

In the heat of the day, at dawn or in the dusk of night,

And if God has still left as a remnant some survivor—

Then perhaps even today your eyes may yet see there,

In the abundance of the shadows of its walls, in the gloom,

In one of its corners or by the stove,

Single ears of grain, like a shadow of what was lost,

Gloomy Jews, faces shriveled and drawn,

Jews of the exile, dragging the heavy yoke,

Forgetting their toil over a worn page of Talmud,

Losing awareness of their poverty in the study of ancient words,

And easing their anxiety with psalms of praise—

(Ah! How base and miserable this sight is

In the eyes of a stranger who does not understand!) Then your heart will tell you

That your foot treads upon the threshold of the house of our life,

And your eye sees the treasure of our soul.

And if God has not taken from you all His holy spirit,

And has yet left some of His consolations in your heart,

And a spark of true hope for better days than these

Still flashes at times from the fissures of your darkness—

Then know and hear, ah, my afflicted brother!

That it is but a rescued spark, but a tiny surviving ember,

Which by miracle escaped from the great fire

Your fathers kept ever burning upon their altar.

And who knows whether it was not the streams of their tears

That carried us across and brought us this far,

And that by their prayer they asked us of the Lord;

And in their death they commanded to us life—

Life unto eternity!

And examine this very, very carefully…

And here I was afraid the Rabbi would answer me, “I don’t know what you mean by absorb the style”….
So Bialik really stayed a Volozhiner, huh? And bottom line, you stayed a Ponevezher…. Much appreciated for the geshmak.