No.
If you re-use the local port, but either the remote host or port changes in the subsequent connection, then this is impossible.
For the case of reconnecting back to the same remote IP/port from the same local IP/port, also known as TIME-WAIT Assasination, there are some rules for the TCP stack to abide by. Mainly - starting out with a higher sequence number than the previous connection. You can read the fine print in RFC 1337. But here's a better link and quote that outlines how the sequence number is adjusted on subsequent connections.
http://blogs.technet.com/b/networking/archive/2010/08/11/how-tcp-time-wait-assassination-works.aspx
In a situation where the server side socket goes to a TIME-WAIT state
and the client reconnects to the server within 2MSL (default TIME-WAIT
time), there are 2 things that can happen:
The server will not respond to the SYN packets from the client because the socket is
in the TIME-WAIT state.
The server may accept the SYN from the client and change the state of the socket
from TIME-WAIT to ESTABLISHED. This is known as TIME-WAIT assassination, or
incarnation of a previous connection.
The key to scenario ‘2’ above is that the ISN (Initial Sequence
number) of the SYN sent needs to be higher than the highest sequence
number used in the previous session. If the ISN is not as expected,
the server will not respond to the SYN and the socket will wait for
2MSL before being available for use again.