No, "Chinese Traditional" refers to the character set used to write each character[1], but the actual text is still written according with the vocabulary and grammar of Standard Written Chinese, which is based on spoken Mandarin.

As an example, this is the sentence "Please give me his book" written in Standard Written Chinese using "Chinese Traditional" characters: 請你給我他的書。

If you use "Chinese Simplified" characters[2] instead, it would still be the same words, but some of the characters have simpler forms: 请你给我他的书。

However, both of those renderings still follow Mandarin vocabulary and grammar. Even though Cantonese speakers generally read and write Standard Written Chinese (in either Traditional or Simplified characters), if they were to actually convey that sentence in spoken Cantonese, it would actually be quite different. Written Cantonese[3] is generally only used in informal contexts, but a rendering of the sentence in Cantonese would instead be: 唔該你畀佢本書我。 (Traditional) 唔该你畀佢本书我。 (Simplified)

The written Cantonese version uses vocabulary and grammatical constructions that are not part of Standard Written Chinese, and Google Translate is currently not able to translate to written Cantonese. I've found that over time though, Google Translate has been getting better at translating from written Cantonese to English (however, for the example I just gave, it appears it still completely botches the translation; it currently thinks it translates to "You shouldn't have let her book me").

[1] https://en.wikipedia.org/wiki/Traditional_Chinese_characters [2] https://en.wikipedia.org/wiki/Simplified_Chinese_characters [3] https://en.wikipedia.org/wiki/Written_Cantonese