Yes, but that slight difference in morphosyntax does not mean that the character-based writing system in use across the Han languages is somehow a burden for speakers of one Han language learning another, as the OP misunderstands.
Not so slight —Cantonese and Mandarin use very different vocabulary. Cantonese also has a lot of commonly used words that don't appear in Mandarin at all, and some that don't even have a character at all. In Hong Kong they use the English letters "Q" and "D" for texting two of those "no character" words.
The Chinese subtitles on Cantonese programs on Hong Kong TV don't actually match the words spoken at all, but the meaning is for the most part similar. This is precisely because if the subtitles did match word for word, no mandarin speaker would be able to understand the subtitles.
Furthermore the whole "it's all the same script" argument only applies to the Han languages, and there's a few more languages in China, including Tibetan, Mongolian, Uighur, Kazakh, Manchu, Hebrew etc. all of which don't use the Chinese characters at all. Which is why it's got a fair few extra scripts on the renminbi notes. Mongolian for example uses the Mongol Bichig (although in the Mongolian People's Republic they also use a slightly modded form of cyrillic, too - introduced in 1946).
And then there's Zhuang, which - in its old-school form - uses Chinese characters and hybrid chinese characters, but would be utterly unintelligible to a chinese reader.
And then there's classical Chinese, which, although using the same characters is also fairly unintelligible to a modern reader, unless they have studied classical Chinese.
But unless they ditch the language wholesale, any tonal form of Chinese is stuck with chinese characters — pinyin doesn't cut it at all, and is only really useful for foreigners to learn mandarin. Context will get you so far, but written down there's no easy way to tell which of the dozen or more characters you mean by the pinyin "chán". Worse still, it only works as a phonetic for mandarin, so it makes no sense to represent the cantonese "Heung gong" as "xiang gang" and even less still with the little tone marks, given that pinyin only has 4 to represent the 5 possible tones of mandarin (4+no tone) when you're using a language with 6+ tones.