I have a video card with dual GPUs on it, but I only use one of them now because my monitor setup has changed. Is there any way that I can setup the additional GPU to be recognized as a CPU for better HD video performance in Adobe Flash or for doing lengthy tasks such as video transcoding?
GPU's design is purely focused on vector and 3D mathematics and thus, can provide little or no help for "regular" CPU's tasks and isn't therefor commonly supported.
However, with Windows 7 and latest breed of DirectX 11 compatible graphics cards, Windows 7 _can_ -- if it sees need for it -- offload some of the computational tasks to GPU, as it can handle GPU and CPU units as one big "computational unit".
One place where GPU "assistance" is in everyday use, is video decoding. Most modern video decoders/tools automagically utilize the GPU for decoding purposes, if the drivers and the card itself support such use.
Thus, the answer to your original question is no. You can't yourself "allocate" your spare GPU to regular computational tasks, at least not yet. But your GPUs can be used by software such as Adobe Flash Player for decoding videos and thus, taking some load off your CPU, if all the bits and pieces are in right place (i.e. the software, the drivers and the card itself support that).