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Do they have the same meaning?

> A: 宿｛しゅく｝題｛だい｝を **して行｛い｝かない** 生｛せい｝徒｛と｝が多｛おお｝いです。
>
> B: 宿｛しゅく｝題｛だい｝を **しないで行｛い｝く** 生｛せい｝徒｛と｝が多｛おお｝いです。
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grammar て-form negation scope
して行｛い｝かない versus しないで行｛い｝く
No, they are quite different.

B is fairly normal, and means 'there are many students who go [to school, I
assume] without doing their homework'. The doing part is negated, not the
going - they still go to school, it's only the homework they don't do.

A can instead be translated as 'there are many students who do their homework
and then don't go'. The going is negated, not the doing; the negative doesn't
extend over the whole phrase.
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Sjiveru is right, but allow me to break it down a bit...

The て part indicates the verb is in te-form ( て形【けい】 in Japanese ). It has
many uses which you can review on your own, but the one I want to highlight
here is how it connects clauses or verbs together. This can be roughly
translate the verb to "and" but also "but" like:

ケーキを食【た】べてコーヒーを飲【の】みました。

I ate cake and drank coffee.

ケーキを食【た】べないでコーヒーを飲【の】みました。

I didn't eat cake but drank coffee.

So, knowing this, let's look at your two sentences.

> **宿題をして** 行かない生徒が多いです。

There are many students who **do their homework** but don't go (to school).

> 宿題をしないで **行く** 生徒が多いです。

There are many students who don't do their homework and **go** (to school).

In each case, I made the **positive** statements bold, so you can kind of see
what's going on. Does this make sense? If not, let me know.
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If sentence A has a comma like:

> A: 宿題をして、行かない生徒が多いです。  
>  B: 宿題をしないで行く生徒が多いです。

then Sjiveru is right.

However, it doesn't have a comma, so they have the same meaning. They mean
"There are many students who go without doing their homework." The して行かない
doesn't mean "don't go" but "don't do their homework."
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2016-01-19T02:36:43.580
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Sentence A:

> A: 宿題をして行かない生徒が多いです。

This almost always means "There are many students who go to school without
doing their homework." (ie, they go to school anyway)

In English, "Don't drink and drive" always means "Don't drive after you
drink", not "Don't drink! Do drive!" Here "drink-and-drive" is treated as one
set. And "Let's not go and see him" usually does not mean "Let's stay home,
and let's see him instead."

Quite similarly, in Sentence A, the ない negates "宿題をして行く" part as a whole.
That's why it's effectively the same as Sentence B.

Other similar examples:

  * 遊んで暮らすな。 Don't live in idleness. (not "Play! And don't live!")
  * 物を口に入れて喋らないでください。 Please don't speak with your mouth full.
  * 物を口に入れて **、** 喋らないでください。 Please fill your mouth with food, and don't speak. (See the comma)
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