Yes, it is possible. It will require ASM though.
First, changing the overworld sprite:
http://www.pokecommunity.com/showpost.php?p=8620314&postcount=465
Second, changing the backsprite:
http://www.pokecommunity.com/showpost.php?p=8522211&postcount=163
And third, you'll need to write some ASM of your own to swap the trainer card sprite. If you understand how the routines above work, you should have no problem doing so.
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