I hope this isn't considered flippant or a violation of the sub's rules, but the short answer is, "No."

For the purpose of this discussion, I'll define "Classical Latin" as Latin written by primarily the native-speaker upper class between roughly 60 B.C. and 100 A.D. in works that survive. This is a narrow definition, cutting out some really influential early writers like Terence and Lucretius and a number of later authors, but I'm going to run with it.

As far as we can tell, Latin has far less slippage in pronunciation than modern languages do; in other words, a "C" is always pronounced like a "C" in the English word "cat." By way of comparison/contrast, think about the pronunciation differences between the English words "tough," "though," "through," "thorough," "throughout," and "trough." [EDIT: I left out "thought."] They all use almost entirely the same letters but are pronounced completely differently. This doesn't happen much in golden-/silver-age Latin.

Ostensibly, that means that it's harder to "get inventive" with the letters you're using, but that doesn't mean that there wasn't significant regional variation in pronunciation, and there's evidence that this (among numerous other factors) affected spelling. Variant forms of numerous words (e.g., "Occ" vs. "Hoc" or "nunquam" vs. "numquam") are attested in epigraphy, literature, and other sources. And I don't have a source on hand for this (I would guess I saw it in the CIL in grad school), but a mix of Greek/Oscan/other characters with Latin ones is evident in Latin inscriptions, most often ones dating to the pre-Classical period. [EDIT: I can't believe I left this out, but there's an entire separate discussion to be had on the evolution/adoption of the Latin alphabet from earlier and foreign writing systems. I'm ENTIRELY unqualified to discuss that, so I'll just leave this here!]

An interesting example of a plausibly deliberate misspelling is the use of "Thybris" (gen.: "Thybridis") in the Aeneid instead of the more typical spelling "Tiberis" (gen.: "Tiberis"). Why would Vergil, a highly educated and splendidly capable writer, misspell the name of The One River In Rome and the deity that represented it? Difficult to say, but his use of Hellenized letters (that upsilon/"I Graeca"), a specific consonant cluster (which, in Greek, would simply be the letter theta), and variant case forms that follow the third declension's pattern for assimilating Greek nouns, suggest an interest in evoking the Greek epics that inspired his magnum opus.

Whether there was a concerted effort to standardize spelling, and the story behind such a (hypothetical) attempt is, perhaps, a more interesting line of inquiry. The emperor Claudius, for instance, introduced three new letters to the alphabet; these lacked staying power, but it indicates some interest on his part to produce or rectify a standard system of writing, whatever ultimate purpose he had in mind. My knowledge of the topic begins to fray substantially here, so I leave it to other (more qualified) contributors to further the discussion.