The double-dash or em dash has many grammatical uses. (
“A unified approach to the proper use of punctuation in English”)In the sentence you presented, it is used to indicate and link to the main clause an abrupt change of thought where a comma will be too weak a punctuation, a semicolon will be dysfunctional, and a period too disruptive to the emerging thought. Functionally, the double-dash is a stylistic as well as a combining and streamlining device for two or more closely related ideas that are better put together in a single sentence.
That particular sentence is, in fact, a fusion of these three sentences:
“The introduction of the law
will be welcomed by thousands of residents.”
“It
will be welcomed in particular by the parents of four-year-old William Whitcher.”
“William Whitcher almost died from eating a peanut butter sandwich on his first birthday.”
The double-dash enables the writer to combine the first two sentences above and avoid repeating the verb common to them (“welcomed”), as follows:
“The introduction of the law
will be welcomed by thousands of residents—and in particular by the parents of four-year-old William Whitcher.”
The third sentence can then be made into a relative modifying clause linked by a comma to the combination of the first two sentences, as follows:
“The introduction of the law
will be welcomed by thousands of residents—and in particular by the parents of four-year-old William Whitcher, who almost died from eating a peanut butter sandwich on his first birthday.”
Now, you were asking if it’s possible to just break the original sentence into the following two sentences:
“The introduction of the law will be welcomed by thousands of residents. In particular, the parents of four-year-old William Whitcher who, on his first birthday, almost died from eating a peanut butter sandwich.”
The answer is no. This is because although the first sentence you suggested is a complete sentence, the second is an incomplete one—a fragment—that has no operative verb. Of course, we can fix the problem by supplying that missing operative verb—by repeating the verb “welcomed in the second sentence, as follows:
“The introduction of the law
will be welcomed by thousands of residents. In particular, it
will be welcomed by the parents of four-year-old William Whitcher who, on his first birthday, almost died from eating a peanut butter sandwich.”
This undesirable repetition of the verb “welcomed” is precisely what the double-dash makes it possible to eliminate in that sentence:
“The introduction of the law
will be welcomed by thousands of residents—and in particular by the parents of four-year-old William Whitcher who, on his first birthday, almost died from eating a peanut butter sandwich.”
