Normita, it probably depends on a number of factors. Usually when I do images that are going to be placed flat on the cake I don't fill the back. When the back is not filled the image is very fragile and thin and also the colors bleed more quickly if the back get wet or greasy. Since the SMBC can be considered greasy you could get problems with bleeding colors and melting RI.
If I were you I would do the RIT not filling in the back and then place it on a strip of fondant as you suggested just to be safe. If you don't want the fondant on there you could instead flip the RIT and flood the back with normal consistency RI. That will also protect the back so you don't as easily get the bleeding and melting.