The Base cooldown is 2.2s and yet does not reduce with item cooldown reduction.
It also does not show when these items are on cooldown in the bottom right.
It might be a little bit much but I think its a good way to combat people just standing near you for the stack and not helping you at all, as well as trying to kill someone for it when it isn't worth.
Bullet Lifesteal, Debuff Reducer, Spirit Shredder Bullets, Long Range, Spirit Sap and both Duration Extender/Compress Cooldown upgrade to T3s. Even if they didn't, I don't really see an issue of why they couldn't
Stats
Upgrades from: Sprint Boots
Upgrades to: Trophy Collector
+2m/s Sprint Speed
+2Out of Combat Regen
Passive
Whenever you score an assist or kill, gain extra health, sprint and passive soul generation. Death results in the loss of 1 stack.
+15 Bonus Health
+0.1m/s Sprint Speed
+15 Souls...