Mixing a Classe 2 channel amp with ice 3 channel ?

It should be fine, afterall you intend on HT use, even for music use it gets a bit blurry about what you are truely going to end up with. I use 2 Classe amps for mains and Rotel for surrounds.

HT theater setups are a huge compromise to 2 channel done well.

Get a powered sub if you need more room filling sound

I use a high end class D amp for my 2 channel listening with a dedicated preamp. I have a lower cost Rotel RMB-1095 SS amp for HT when I watch movies which isn't too often. No problems with the combination or sound across the center, surrounds and rear backs blending in well. I have a dedicated processor for HT and the preamp has a HT by-pass.

HT isnt a compromise when doen right, for instance my Projector and screen are not in the way for music listeing.