Yep - the smaller (2"x2") Cuttlebug dies work perfectly in the Sidekick. Use them exactly the same way you would a Sizzix Sizzlit die - make a 'sandwich' - from the bottom up:
clear mat
CB die foam side up
paper or cardstock
second clear mat
then roll through your Sidekick.
You can also use the small CB embossing folders in the Sidekick - the ones that come in sets of 4. Just place paper or cardstock in the folder, sandwich the embossing folder between the 2 clear mats and roll through.
Have fun!