Looking at a thing on Old Chinese, you'd think that the entire language was like Arabic or something like that, since Old Chinese had sounds that the modern Chinese regionalects do not have - things like /ɣ/, the voiced velar fricative and the like. Also, Old Chinese grammar was definitely not like Modern Standard Mandarin Chinese grammar. If Siddham was applied to Old Chinese, Chinese would've evolved differently than in OTL - who knows, maybe Chinese would not be tonal at all but would still be difficult for Westerners because of some sounds that would be difficult for them, not to mention a grammar that would be daunting (I'm thinking if something like the Austronesian alignment being widely used, for example). Plus, there's the task of modifying Siddham to match Old Chinese phonology - for example, the pharyngealized consonants.
If Old Chinese is written using an adapted Siddham script, I have a feeling Modern Chinese will be similar to Modern Tibetan in that it will use a writing system derived from an Indic system and possibly have a spoken language that has done away with all the complex consonant clusters while keeping them in the writing system.