You should be fine,
I use a Zoom H4N and marry the audio to DSLR video of varying frame rates without issue.
The Zoom doesn’t record timecode. Like all audio recorders it keeps time by sample rate (some audio recorders will add/sync TC, the Zoom H4N is not one of them.) What you want to do is set the zoom to sample at the frequency of your timeline settings (48khz is typically the way to go) If you record 44.1k you may see drift over time when you add it to a timeline that is set to 48khz.
Bit-depth is not as important for sync. It’s importance lay in sound quality.
Colin McQuillan
Vancouver, B.C.
“Live, love, laugh and be happy.”