It won't work if it has a bad VRAM. And depends on the software used to mine.
Reaper use the system RAM for mining, while cgminer is using GPU RAM. But they all use at least 2gb of VRAM
Ex:
4 x 7970 are OK with 2GB RAM if using cgminer, but for reaper you will need around 8GB.
With the scrypt parameters used in litecoin’s implementation (N = 1024; p = 1; r = 1), each thread needs about 64-128 KB depending on the lookup_gap and thread_concurrency settings when mining with a GPU. This makes litecoin actually ideal to mine with a GPU, GPUs have very fast memory (bandwidths going into hundreds of GB/s) and generally 128-512 KB RAM per stream processor.