Noob question about supervision of lan routeur interfaces

Hi all,

First sorry for my bad english (french people are not famous with english language ^). I'm wondering about the possibility to ping a LAN interface of a router when this one (the interface) is UP/DOWN. I specify that we ping from outside, not from the router himself, like a "entreprise supervision" configuration. For you, is it possible ? And if not, why ? Because the network in which belong the interface is no longer announced ?

Thanks :)