It's definitely possible. The Austronesian Tsat language of Hainan developed tones from being in close proximity to tonal languages(Chinese may actually have picked up tones from its neighbors as well), so a simplification of verb conjugation might happen as well.Hmm. Can an Indo-European language lose its conjugations over time? Is that a likely effect from prolonged contact with something like Old Chinese?
Simplification would definitely help. The Chinese writing system works reasonably well for Mandarin, less so other Chinese languages, and really doesn't work all that well for Japanese (aside from Sino-Japanese words). What you'll get with the writing system in the link is something like the Japanese writing system were you have Chinese characters followed by symbols to mark verb endings. If you're gonna have symbols representing sounds, why not do away with the characters entirely? Japanese can't anymore due to the sheer amount of homophones, but the hypothetical Chinese Indo-European language would be borrowing Chinese words (if at all) from a language with fewer homophones than when the Japanese did the borrowing. Writing in a purely phonetic script is simply easier with non-Sinitic languages, although coming up with a syllabary for an Indo-European language is quite daunting as well since you'd need at least several hundred. It's quite possible to do though. The Yi people use nearly 800 symbols in their syllabary and their writing system has endured since the Tang dynasty. The fact is, there would be no easy way of using Chinese characters to write another language as unrelated as an Indo-European one, but then again unwieldy-ness and complexity has never stopped people from using a writing system.Would it really be that much worse than written Chinese is now? Leaving out irregular conjugations, would you need more than a couple of dozen additional symbols? And would it help if the inflections and conjugations also ended up becoming more simplified over time?