No, the production of nitrate indicates that the bacteria that deals with nitrite are multiplying or not.
Excluding plants and other by process. At any stages of the cycle, if no nitrate is produced, nitrite are not really being processed and will build up if no other exits are available.
In a fishless cycle you can have situations where nitrite is converted faster to nitrate than ammonia to nitrite. And it result in nearly direct nitrate rise.
You could easily wait for ever that nitrite rises while Nitrate is already building severe level.
At some point... Checking for nitrate during the end of a fishless cycle is in my opinion the only way to see that you are completing the loop.
I'm far from a chemist, but a good mathematician. And basic comparison made me consider 2 points.
Both are very different critters. And the major factor in their development are dead pan water chemistry that is out of your control at least 50% of the time.
It could go from both have difficulties, to both thrives at the same time. But most of the time it's one or the other. But once established...