You could. I think most brands, if there's an image on the backup/loading media, just load it. That's what Siemens does, although in their case you have to dedicate a given SD card for transferring program, additional memory, etc., whatever it's going to be used for, so on power up the PLC already knows the SD card is transfer type and just loads the project.
If you did that, it would be like PLCs equipped with program backup EEPROMs that if one is present on power up, automatically load the program, sometimes depending on the settings in the PLC. A SLC, for example, has several levels of eagerness to load from the PROM, Always Load, Load If There's No Program in RAM, and so on.
If you do implement that (fully automatic mode), there should be some kind of option for not loading data along with code, in case it's a normal power cycle with an already running PLC, and the SD card is just there for emergency program backup.