Hi,
I'm using an old (but stable!) version of Cubase, and was recently experimenting with Curve EQ.  Unfortunately, I ran into some latency issues.

I placed Curve EQ as an insert on a channel.  On playback, this channel was definitely out of sync with the rest of the tracks, which is understandable due to Curve EQ's high latency.  But when I exported the mixdown of the song, the affected channel was still out of sync in the resulting exported file.

That puzzled me, because when I use other high-latency plugins, latency is not a factor when exporting a mixdown, it's only evident during real-time playback.

Is there a way to avoid Curve EQs latency during the export process?

Many thanks!

No, it's impossible to avoid it.  Host should take care of it - I suggest you to use latest hosts.