Not really. You can try to hack it around by using Element#computedStyles() but it might get tricky because some styles might get stuck in the "style" property and override CSS if the element change its context.
Much better solution would be to define CSS3 transitions in your CSS classes and then simply add them with Element#addClass. That won't make a smooth transition in old IE browsers, but it will be a less error prone approach. Besides that will be much simpler to support.