No.
Now the long answer: Internet Explorer does not lend itself well to being styled. You will be able to set a background image for the left-hand side (the text content) that has rounded corners, but the drop-down arrow will be fixed as the default browser. You'll also find that the mousedown and mouseover states for the control will be fixed as the default style.
I think that in many cases, the ideal preferred design needs to be a little pragmatic about limitations in browser standards support. Specifically, the problem that IE6 doesn't support a fair number and IE7 is only slightly more compliant.
Sorry for the bad news.