Is there such a feature? The executable would be run if found after the usual boot time mounting. Preferably standard Unix filesystem path; for example,
(hd0,0)/root/autorun.sh. This can be useful with live CDs.
I don't think the kernel would do that. It can't know how and when to start the process, since the boot-time actions like mounting all filesystems are done in userspace, and the kernel can't know when it's done.
But the kernel command line is visible in
/proc/cmdline, so you could create a tool look for a particular parameter there, and then start the named program. You could then start that tool in some system-level startup script that runs late enough (like
/etc/rc.local), or in the live user's X startup files if you want to start a graphical program.
In any case, you'll need to create your own live-CD to include that.