EDITED:
My questions is more about whether or not MongoDB will keep the index on RAM always, assuming that there is enough space. Because actual data is pushed off of RAM if they are not recent to make room for more recently accessed data. Is this the case with indexes as well? WIll indexes be pushed off of RAM based upon recency? Or does MongoDB treat indexes with priority and always keep it in RAM if there is enough room?
That is not guaranteed.
MongoDB does store indexes in the same cache as documents, which does evict LRU.
It does not load the entire structure into memory, it load pages as they are needed, so the amount of the index in memory will depend on how it is accessed.
Indexes do get a bit of priority, but that is not absolute, so index pages can be evicted.
An insert into a collection will likely need to update all of the indexes, so it would be a reasonable assumption that any collection that is not totally idle will have at least the root page of each index in the cache.