The type of attack you are describing is a congestion attack. In theory, the simplest form of such an attack would be a general DoS on the Tor network.
Taking things one step further, a congestion attack could be used in conjunction with traffic correlation to monitor a given user of the Tor network. Such a strategy is discussed in A Practical Congestion Attack on Tor Using Long Paths (section 2.2.3).
To mitigate such attacks, as of Tor version 0.2.1.3-alpha, the maximum number of hops is restricted to 8, regardless of what is set in the client code. This is done by restricting the number of "relay early" cells that a client can send when creating a circuit.
[A Practical Congestion Attack on Tor Using Long Paths, Section 5: Proposed Solutions]
In the modified design, Tor routers now must keep track of how often
each circuit has been extended and refuse to route messages that would
extend the circuit beyond a given threshold t. This can be done by
tagging messages that may extend the circuit with a special flag that
is not part of the encrypted stream. The easiest way to do this is to
introduce a new Tor cell type that is used to flag cells that may
extend the circuit. Routers then count the number of messages with the
special flag and refuse to route more than a given small number (at
the moment, eight) of those messages. Routers that receive a
circuit-extension request check that the circuit-extension message is
contained in a cell of the appropriate type.