You won’t receive SMS in the “iMessage app”. Messages is the iOS messaging app, it has the ability to send messages via SMS or iMessage.

If the iMessage service is enabled and the recipient has an iMessage address/account, it’ll send the message via iMessage. Otherwise Messages falls back to sending a message via SMS.

I know, we don’t usually make a distinction about Messages the app, and iMessage the service, and just say iMessage.