Your write will be fine; that is, it's not as if data from one write will be interspersed with the data from another write. It's just that the order might be wrong, or opening the file multiple times (possibly from multiple processes) could be fun too. The program or computer crashing mid-write can also cause problems. Things like that.
Again, may not be an issue at all for loads of applications. But I used a lot of "flat file databases" in the past, and found it's not an issue right up to the point that it is. Overall, I found SQLite simple, fast, and ubiquitous enough to serve as a good fopen() replacement. In some cases it can even be faster!