Only if your schooling has exposed you consciously to the vocabulary and grammatical structures of written Chinese that differ from your regional dialect, as it surely has. Lessons in literacy in vernacular Chinese literature ( 白話文 ) are in part lessons in the spoken grammar and vocabulary of the language reflected in that literature, which these days is usually Modern Standard Chinese.

If we had a phonetic alphabet, it would be nearly impossible to communicate in any kind of written medium.

The experience of Western cognate languages suggests that people can always more readily communicate in writing in sound-indicating scripts than they can speak over the telephone. After edit: for example, I have read several Spanish-language letters that came randomly to business offices I worked in, without any formal course in Spanish, but I would certainly have great difficulty carrying on a conversation in Spanish.

Long term changes aside, a phonetic script would make learning standard Chinese and dialects faster, so children could learn both their local dialect and the government standard (Mandarin) as part of their schooling.

The main problem with a phonetic script would probably be the varying phonetic inventories of the different dialects/languages within China. I'm not sure if you could make a phonetic script that would work beyond the main dialects.