You do not start a new rampage as long the old rampage animation is going (it is actual a 4 hit channel ability), so it might feel a bit akward, but if you click and spellque the rampage, you will do two rampages in a row without any real delay. Both GCD and Rampage hit-animation are sped up equally by haste.
So yes, you might feel nothing happens when you click rampage, rampage, with enough haste - yet that is just the animation starting kinda slowly so it feels clunky. RPS/DPS is not affected, don’t worry.
So to clarify:
You cast rampage, into raging blow:
What happens - You cast Rampage, during end tail of the channel you cast raging blow, it feels snappy, but after the instant RB animation you feel there is a gap between animations again.
R1, R2, R3, R4+RB
You cast rampage, into rampage:
When you rampage, rampage, during the end tail of the 1st channel, rage is consumed and the spell is qued, the channel continues straight after the first, it feels a bit slower but costs the same GCD slot and ends at the same events (as the Raging Blow you cast at the end of the next Rampage will be as in the prior case, instant and during). Animation looks a bit wonky, but all is good in the hood.
R1, R2, R3, R4+R1 (with visual delay)+R2+(sped up)R3+R4(delay ends). The more haste you got, the weirder this looks.
If you want to test this out in action ingame - go Rav+Spear, for the rageregen, you want the autohits to hit right after the first rampcast to gain this effect. Quite easy to replicate.
I play Nelf, so will never have any animation issues, so you can go and hit dummies for a while and see what happens - maybe there is some bug for Orcs/Tauren.