Sort of. Indonesian had Jawi, based on the Arabic script. People in today's Vietnam mostly wrote in Chinese AFAIK. Those methods of writing were dominant among the people who could write. But the populations were mostly illiterate, so it was easy for colonial administrators to supplant the existing writing systems with Latin as they introduced European-style schooling.

How well do Chinese characters mesh with Vietnamese?

I mean I note that there are some Chinese languages, with millions of speakers, where the largest written text they have is a bible written in a Roman script. If those are a challenge surely Vietnamese must be as well.