I believe that dust and non dust are handled the same, and also I think it is important to be aware that the definition of dust changes as the value of BTC increases (or decreases).
I would think the definition would take into the account the value of BTC changes as it relates to fiat as part of the definition.
The blockchain itself is just a list of transactions (grouped into blocks, with a header for each block).
Transactions are just a list of inputs that are being spent, and a list of outputs indicating what address now has control of the value.
There is no special handling of "dust" in the blockchain. They are just outputs.
Clients (or wallets) on the other hand may have special handling of "dust". Some wallets my refuse to display any dust outputs associated with your addresses. Others may handle the spending of "dust" outputs poorly and result in excessive transaction fees on any transactions you create. Some wallets may refuse to relay transactions that have "dust" outputs.