Cast baseboard + copper fin on the same zone?

does copper baseboard heat up faster than cast iron baseboard?
I would think it does.
Is the copper baseboard near the thermostat? If so could the thermostat be satisfied from the heat coming off the copper baseboard and the areas or rooms with cast iron baseboard be cooler than they should be.

As @STEVEusaPA says -- no reason they can't -- if they are sized properly. Any baseboard or whatever construction -- for that matter, any radiator -- will produce X BTUh of heat when fed water at a temperature of Y, and that rating is given for the radiating unit -- and is independent of the material of construction. The rating is given as the EDR -- equivalent direct radiation -- and a unit with a certain EDR will produce the same amount of heat as any other unit with the same EDR in the same setting, regardless of material.

With that said, as @bob eck speculated, there is a real difference between cast iron, finned steel, and finned copper for baseboard, and that is related to the material. In that order, the former will heat up to temperature much more slowly than the latter -- and, correspondingly, cool down much more slowly. This doesn't affect the total heat delivered, only the rate at which the rate increases or decreases with time. This may make a difference in the perception of heat from the unit, but also makes a difference in control -- as he says, if the control thermostat is in a space with copper fin, it may be turned off sooner than might be needed for another space on the same loop which has cast iron.

It's a bad idea. The only time I've seen it work is on a system with constant circulation and a good outdoor reset system.