It doesn't look promising. The following was as close to an option along the lines your looking for that I could find.
curl didn't offer anything better.
I'm pretty sure that timeout (countdown) was designed to thwart exactly this type of activity.
Set the network timeout to seconds seconds. This is equivalent to
all at the same time.
When interacting with the network, Wget can check for timeout and
abort the operation if it takes too long. This prevents anomalies
like hanging reads and infinite connects. The only timeout enabled
by default is a 900-second read timeout. Setting a timeout to 0
disables it altogether. Unless you know what you are doing, it is
best not to change the default timeout settings.
All timeout-related options accept decimal values, as well as
subsecond values. For example, 0.1 seconds is a legal (though
unwise) choice of timeout. Subsecond timeouts are useful for
checking server response times or for testing network latency.
Set the DNS lookup timeout to seconds seconds. DNS lookups that
don't complete within the specified time will fail. By default,
there is no timeout on DNS lookups, other than that implemented by
Set the connect timeout to seconds seconds. TCP connections that
take longer to establish will be aborted. By default, there is no
connect timeout, other than that implemented by system libraries.
Set the read (and write) timeout to seconds seconds. The "time" of
this timeout refers to idle time: if, at any point in the download,
no data is received for more than the specified number of seconds,
reading fails and the download is restarted. This option does not
directly affect the duration of the entire download.
Of course, the remote server may choose to terminate the connection
sooner than this option requires. The default read timeout is 900
Altho you might be able to script up something like this:
# an attempt to pause long enough for countdown before opening an accept port