does this in anyway damage the network?
Not really damage per se, but it can cause bloat and it is unnecessary. It'll also make recipients have to pay more as transaction fees, so it is an annoyance and 'damaging' in that way.
Recipients do not have to pay higher TX fees if they receive this dust spam as they can simply ignore these inputs and choose not to spend them.
I do agree that it does bloat up the blockchain and adds additional data that the nodes need to store, however this spam does provide valid and needed income to the miners