Souperman, I am not sure if you mean any text sent by the user.
It could be a line sent by programming (scripting), not manually typed by the user.
In case you are referring to the later (manual typing) then mIRC (as an irc client) does allow you to trigger on own text.
If it's the former you're talking about (lines sent by user as a result of a code getting executed) then I agree with you, I have never seen any irc client that allows triggering on own text either.
The following example is taken as is from mIRC help files:
The on INPUT event triggers when you enter text in an editbox and press enter.
Format: on <level>:INPUT:<*#?=!@>:<commands>
Example:
on 1:INPUT:#mIRC:/echo You entered the text " $1- " in the #mIRC window
<font size=-1>[ This Message was edited by: z_one on 2002-05-27 07:29 ]</font>