This +1
If your system is rapidly converting ammonia to nitrate you can add fish. As Randy points out, nitrites are terrible for fresh water fish, not so much for salt water. The chlorides in the water block the fish from absorbing nitrites. The other reason not to worry is that hobby level test kits aren't exactly accurate. Too many issues to cause false positives.
If you have ammonia dropping and nitrate climbing there are only two options. Either the nitrites are being converted to nitrate and it is a false positive or you have a massive number of nitrospira bacteria converting ammonia directly to nitrate. Either way, you are fine to add fish.
