Can memory access be detected via fMRI? Can the use of memory, in it's various forms (working memory, procedural, semantic), be detected and distinguished from one another via fMRI?
In theory, yes, because there are now many theories, supported by evidence, which map different memory processes onto different regions and patterns of activity in the brain.

In practice, there are many difficulties with doing this. First, it would depend on what stage or process you are thinking of (are you considering encoding? or retrieval?). Second, many subtypes of memory are defined according to the stimulus (for example whether you are remembering facts or actions), and so differences in brain activity might be due to the stimulus and not the process per se. Thirdly, fMRI has limitations which might make it difficult to isolate the relevant differences, especially if you were trying to do this on a trial-by-trial basis or if you were looking at subcortical structures.

There are plenty of papers which try and address this. For example, here is one looking at dissociations within recognition, here is one in Alzheimers and here is an influential review.