In that case being able to show arbitrary other text would definitely be a hindrance because the scanning software typically looks at the data stored in the database. However I think you don't need a Turing machine to exploit this — you could have a single ligature in a well crafted font produce a full paragraph of text.
Perhaps there's an alternative vector where someone's premade font on a site that doesn't allow font uploading can be exploited to make arbitrary calculations given certain character strings. Maybe bitcoin mining, if you could find a way to phone home with the result
If this font format is successful, then given enough time, it will become legacy. People won't be as vigilant about it, and they won't understand the internals as well. This is why TIFF-based exploits became so common 20-30 years after TIFF's heyday.