Does removing the comma before 'which' etc in a non-restrictive clause change the meaning of the sentence?

There are many 'rules' on the net saying that a comma should be placed before the relative pronoun 'which' in a non-restrictive clause. (http://www.oxforddictionaries.com/words/relative-clauses)

But would the sentence have the same meaning without the comma before the relative pronoun?

Does omitting a comma before a relative pronoun change a nonrestrictive clause into a restrictive clause?

For example:

'We ate the pizza, which was nice.'

'We ate the pizza which was nice.'

If so does the same apply to relative pronouns other than 'which'?

Solution 1:

If you omit the comma, the relative clause is likelier to be read as restrictive: you had a number of pizzas to choose from, and ate only the nice one. The distinction between restrictive and non-restrictive relative clauses depends more on that comma than on the choice of relative pronouns, and many now dismiss as a superstition the idea that one should use which for non-restrictive and that for restrictive (but who for both where the antecedent is one or more persons). The most emphatically restrictive form of the relative clause even uses which as its relative pronoun by preference, that having already been used as a demonstrative:

We ate that pizza which was nice.

Solution 2:

In addition to what others have said, have a look at this article by Donald Knuth. Look for the term wicked whiches. (The sermon intentionally oversimplifies, because it can sometimes be helpful to do so.)

Rule 22. Don’t say “which” when “that” sounds better. The general rule nowadays is to use “which” only when it is preceded by a comma or by a preposition, or when it is used interrogatively. Experiment to find out which is better, “which” or “that”, and you’ll understand this rule.

• Bad: Don’t use commas which aren’t necessary.

• Better: Don’t use commas that aren’t necessary.