Would the sentence above be an example of an author making stylistic error on purpose?

The two excellent comments from Dan Bron and StoneyB have given you your answer: the famous quote from A Tale of Two Cities is an example of a skilled author making a stylistic choice, not an error. As Dan Bron noted:

"Certainly it's deliberate, no question of that, but I'd opine that the primary device being employed is anaphora, rather than the comma splice."

To which StoneyB added:

"The 'rule' against comma splices does not reflect the facts of English grammar; it is a 'baby rule' imposed by teachers upon learners (native and non-native) to discourage misapplication in ordinary prose of the ancient and effective rhetorical device the ancient Greeks called asyndeton. It's perfectly OK to use it if you know what you're doing."

This Dickens quote is also used as an example of a balanced sentence.

[All credit for this answer goes to Dan Bron and StoneyB. Thank you to both.]