What modelling amps like your Spider II are trying to sound like is a raging tube amp, with studio effects applied to the sound picked up by a microphone placed in front of the speaker.

As magicninja says, about the only safe way to introduce those effects would be from the preamp of the Spider into an Effects Input of an effects loop, or to the amp input.

You can't connect the Spider speaker output to anything but a speaker, unless you have an attenuator of some kind to reduce the signal level to something that your new amp can handle. And even then, you would be putting at least some of those effects into the wrong part of the signal chain.