Nope.
The Outlook vulnerabilities are based on its integration with Internet Exploder...errr...Explorer. Since Eudora stands alone, untethered to IE or internal Windows code, it is basically immune to these attacks.
I have been using Eudora for many (6? 7?) years now and have never been affected by a virus, even though I have received many via email.
Who says being a monopoly is a good thing? :P