Most likely not, I would imagine.
It would be best to export your Illustrator based graphics using the "Save for Web & Devices" as a JPG or as a GIF if you want transparent boarders around the graphic. I don't know for sure, but would hazard a guess that Muse would default this kind of cut-n-paste into a rough JPG, hence the white box.
If you use the "Save for Web & Devices" route, you can control the amount of compressiona and the quality from this route as well. As has been previously documented, allowing Muse to decide on what method to crop and save your images and graphics often results in less-than-prime results. It only takes another minute or two to do it the 'long' way and get a much better result.
While you can cut-and-paste from AI into ID, this isn't best practice either.
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