In a simple one word answer, NO.

As you are most likely aware you would have mismatched impedance loads that would harm your equipment.

Most 4x12's are 16 ohm mono and most 2x12's are 8 or 4 ohm mono loads (d0n't worry about the stereo qualifications for now)

On your SpiderValve you can run only run one set of 8 ohm cabs, meaning two 2x12 cabs that are an 8 ohm load each(I just checked the amp back photos on here as I have the HD100mkii head).

The only way to run the speakers in your SpiderValave and a 4x12 at the same time would be to have an amp guru wire your 4x12 to be 8 ohm mono.

Wait a tick, I just noticed from the picture on here the speaker cable is plugged into the 4 ohm single meaning your amp must have two 8 ohm speakers making it a 4 ohm load. Sorry, I'm so used to seeing the two 16 ohm Vintage 30's in the back of my Mesa I took it for granted the SV used 16 ohm speakers as well. So in a sense you're screwed even more now with trying to do what you wanted. From what I can ascertain the only thing you could do would be to hook up your 4x12 by itself to your SpiderValve using the 8 ohm stereo inputs on your 4x12.

So to put it back into easier terms, no you can't run them all together on the SpiderValve, but you can run a 4x12 by itself if you wish using your amp just like an amp head.