We did this for a client once, and while it is technically possible... I have to say, I strongly recommend against importing the entire LCSH vocabulary into your AtoM instance. The sheer size of it makes it unwieldy from a data load perspective, a performance perspective, and also an end-user usability perspective.
In terms of loading it, I wasn't directly involved with the project, but I believe it took a bit of hackery, and throwing a lot of system resources (memory in particular) at it to be able to get it to import at all.
Performance wise, once you start having hundreds of thousands of terms in a single taxonomy, it can become difficult to manage. Most of AtoM's functionality is still performed synchronously - that is, via the web browser in real time once an action is submitted. Browsers tend to have a built-in timeout limit of about 1 minute, to prevent long-running tasks from running endlessly and/or consuming all available client resources. If you tried to edit a term deep within a hierarchy that had thousands of children and siblings and potentially many levels of terms above it, odds are high that the web browser will time out before AtoM can make all the necessary updates to the related terms if you start editing the preferred form of name, for example.
From a usability perspective, it became a nightmare for both archivists and researchers. The institution in question found that it rendered browsing by term virtually useless for themselves and the public - the vast majority of terms were unused and the LCSH SKOS file rarely if ever includes scope notes, so you end up with thousands of pages of results with no related descriptions showing up. Similarly, finding the right term to link in the autocomplete dropdowns on descriptions (i.e. subject access point field) became very difficult.
There are likely other gotchas as well, but as I mentioned, I wasn't directly involved with this project. In the end however, we are currently working on a project with the client to remove LCSH and replace it with a locally modified version of
FAST topical terms instead, which is much much leaner.
I personally think it much wiser to use LCSH or other large controlled vocabularies as guidance, and to create a curated subset of terms locally for use. You can still use the sourceNote field to link them back to the source vocabulary, but this way you are not overwhelming your staff and researchers with a huge and largely unused list of terms.
Just some food for thought.