'draw them into' is correct and usable in written English.
It implies a kind of persuasion or influence. For example, "The compelling argument drew them into the debate."
"Ned teaches us to engage undergraduates by asking questions that draw them into each object.
You want to give them music to draw them into the whole story.
It hopes this will draw them into the formal economy.That has caused lots of grumbles.
In describing his brothers, moreover, he fails to draw them into vivid, complex, dynamic characters.
They believe it will ultimately draw them into a war with Nicaragua, which most oppose strenuously.
He waved menus at passers-by, trying to draw them into the restaurant, where he works.
Earn the love of the assembled throng through laughter, then draw them into your world.
There has been an attempt to draw them into the healthcare system through some basic training.
But the good news for buyers is that they can expect better deals to draw them into the showroom.
"That's very good practice for writing, if you can draw them into a mystery in the same way.
As we see interesting stories emerge over the next week, we'll be sure to draw them into this comment thread.
