The tsunami itself wouldn’t need to be a mile high if the entire ice shelf on Antarctica slipped into the ocean. Ahead of the wave would be the most violent storms as the atmosphere was compacted and pushed forward. Water would gather and swell at every nook and cranny available on the earth. The sloshing from the wave across the globe could easily last 40 days before settling; leaving behind thick mud perhaps a mile deep. It’s not only possible, but plausible.
I would concur only if it were a direct causation linked to the event which formed the mid-oceanic trench (i.e. Noah’s Flood). Of course this event takes about a year for dry land to re-appear not just 40 days. The flood was 40 days of rain but took much longer to bury the fossils and recede.