Interestingly we were working with a start-up which was trying to go in the other direction. They want(ed) to locate RAM in dedicated servers away from compute, rather like storage is today centralized in NASes. Of course it requires insanely fast network interconnects.
(I'm not claiming this is a good idea, I'm actually rather sceptical, but pointing out that there are companies trying this)
In some sort of technical sense, yes; it's made out of SRAM and one could have the cache be mapped exactly to a block of memory that is the same size as the cache.
In a practical sense, no, because it's structured as cache and accessing it is more convoluted than direct access to a bare block of memory. See https://en.wikipedia.org/wiki/Cache_placement_policies for a description of the various types of cache structures.
If you never loaded addresses outside of the cached memory locations either explicitly or speculatively then without invalidation you could run entirely in L3 so it would be serving as storage rather than cache RAM.
(I'm not claiming this is a good idea, I'm actually rather sceptical, but pointing out that there are companies trying this)