Is multi-level ConcurrentDictionary still thread-safe?

Question

I have four level data structure defined like this:

Dictionary<Type1, Dictionary<Type2, Dictionary<Type3, List<Type4>>>>

The whole thing is encapsulated in a class which also maintains thread-safety. Currently it just locks whole collection while it reads/manipulates the data (reading is by orders of magnitude more common than writing).

I was thinking of replacing the Dictionary with ConcurrentDictionary and List with ConcurrentBag (its items don't have to be ordered).

If I do so, can I just eliminate the locks and be sure the concurrent collections will do their job correctly?