The answer for "normal usage" for a discrete/PCIe/AGP/etc. GPU is simply: "no" and the reason is that it is a physical wired issue as the CPU doesn't have the same access to it as with DDR RAM plugged into the motherboard (I'm not going to go into the details with NUMA but it's the same issue, just a tad different)
The comment about GPU RAM as swap will provide you "virtual ram" that should be faster than USB/SATA/disk based virtual RAM... it called swap space/paging file etc. depending on the OS in use.
HOWEVER the question as asked mentioning "dedicated" and "shared" is indicative of APU/onboard/onchip type GPUs and that is different, as they actually DO share the CPU's RAM, and there you have options in BIOS/etc. to set how much of CPU/GPU shared RAM is allocated to the GPU (and thus not "available" for the CPU)