Someone who's literate in Chinese would only be able to infer the meaning of an unfamiliar character if they already knew all of the surrounding characters. Then, you can guess the meaning of the character based on context, and possibly hints from the character itself about pronunciation and/or meaning (though this is very hit-or-miss, because many characters don't contain obvious hints). In order to reliably know all of the context surrounding a character, you need to know about 3000 characters total (that's the point at which you can recognize 99% of characters on a page). This is still a very tall order, which takes years of study to achieve.
The Chinese characters do indeed contain semantic information that Pinyin (the standard Romanization) does not, but in practice, you don't need that extra semantic information. If you write down a single word in Pinyin, it may have a few homophones, whereas the same word, written in Chinese characters, would be unambiguous. However, in written Pinyin texts, you would almost always be able to figure out which word is meant from context. In the few cases in which that would not be possible, the author could slightly rephrase the text to make it unambiguous.
Most languages on Earth (that have a writing system) are written using alphabets. Chinese is not so special that it could not be written using an alphabet as well. The reason why China hasn't switched to an alphabetic script is because of cultural attachment to the script, not because the Pinyin doesn't work just as well in a practical sense.