I shot limits up until the last week of the season last year. I've seen some places that were amazing one week and crap the next and vice versa. Last year we just hit it right and had white-wings and ringnecks early and about the time they started to slow we had a huge influx of mourning dove.
So to answer your question it depends on the place. It's possible it could be even better two weeks after the opener.
We don't manage our property for dove so limits are pretty rare on opening day/weekend. But we see pretty healthy numbers by the end of September and into October as the migrators apparently use our wooded area as a roost. The "Kansas birds" are a real thing.