Testing Navori Passive on Shyvana

Results:
W can be maintained indefinitely with no additional AS or haste. Normally you need 70 haste.
E mark can be maintained at level 9 with E maxed with no additional AS or haste. Or really close to that. Normally you need 60 haste.
Q (maxed) will be up after two attacks with 25 to 45 haste based on level (at least 13) and additional attack speed. Normally takes 70 to 115 haste.
Dragon Q is fully refunded vs 4 targets at 8 haste. Normally you need 50 haste. 20 haste would normally work for 5 target, Navori does that alone.
Dragon Q vs 3 targets is fully refunded with 55 haste. Normally takes 100 haste.
Resetting Dragon Q vs 2 targets would take an unachievable 300 haste normally. It is possible with Navori and 138 haste, but the build needed for that is entirely impractical.

I recommend thinking of Navori passive as 45 haste in the situations where it works. Ideally you would have enough haste by 3 items to have Q come up after two attacks. With Navori haste beyond 55 does not really do much for you. And 55 haste on top of Navori should usually be treated as a luxury goal to hit in the game goes really late or you get Hex Dragon stacks.

To actually be worth building, Navori needs to allow other adjustments to your build from needing less haste elsewhere to hit significant milestones.

And it is more likely you can use it the more melee champions there are on the opposing team.