The transactions will likely never be included in a block, as they do not meet the defacto bitcoin transactions rules for transactions sent without a fee, detailed here:
A transaction may be safely sent without fees if these conditions are
It is smaller than 1,000 bytes.
All outputs are 0.01 BTC or larger.
Its priority is large enough (see the Technical Info section below)
*Copied from https://en.bitcoin.it/wiki/Transaction_fees#Sending*
Since the transactions fail to meet the criteria to be included in a block for free (which is already getting rare), the transaction will likely be rejected on most/all mining pools, though may be rebroadcast by the sender or the receiver. The transactions may remain unconfirmed for a long time, unless the sender double spends his inputs, nullifying the transactions.
The attack is similar to a ddos on the bitcoin network, as the transactions propagate through the nodes which accept and relay the transactions. This does not cause issues with the '7 transactions per second rule' as the transactions will likely not get into a block, but may cause latency if enough of these transactions are broadcast.
It's more of a pester than a malicious attack.