This is a gif saved for web from photoshop. I'm not sure how to add the patterns to the clothes in Adobe illustrator. The only problem is, that you may have low quality of pattern printouts, particularly if you want to enlarge the logo.

These two (in different sizes) are gifs saved from illustrator. The beauty of a vector illustration is that you can enlarge and reduce size without losing quality, so they work well in printouts or on the web. That is one reason why logos are created in simple shapes / forms.

When you start adding pixel based images / photos, it is harder to retain quality printouts. But this (above) would definitely be fine if used just for the web and possibly ok printed at this size.