No. Timing out is when a specific time limit is placed on an operation and the time expires. An example of a lack of a time out is when a disk I/O operation at a low level on a SCSI disk has no time outs specified at the adapter level communicating with the hard drive, and never responds locking up a system (I/O channel). In this case, the only resolution is to recode the SCSI bus adapter software with timeouts on the I/O commands to the hard drive.
If a ping does not reach a host, the proper question to ask is why? A knowledge of the time of when a connection starts to have a problem is not as valuable a piece of information as why it is having a problem - then when you know, it may be possible to do something about it.
On my dialup, almost daily I can usually tell when my connections are having problems - and shortly thereafter my modem will hang up based on no response to 4 echo requests which is the configured limit (or timeout) on the modem determining to hang up and reconnect.
A ping usually does not work when a website is either overloaded and cannot respond or has severe problems which cause it to be unavailable.
-- Tom