Well, yes, you can. If your AD should just be available inside the EC2 cloud, then you 'only' need to adjust the Security Groups (i.e. firewalling) between the nodes.
If you want the AD to reach into your own on-premises server park, then you'll need Amazon Virtual Private Cloud, which is a VPN between Amazon and your own servers.
Additionally, Amazon has a nice overview of how Windows is set up in their environment.
Regarding whether it's a good idea -- in most cases I would say "no". For these reasons:
Machine settings are not persistent across re-spawns. This could be worked around with redundancy, persistent data storage for each server, and some scripting.
EC2 servers can just suddenly disappear without warning (when the host server goes down). In practice this happens more often than you might think (i.e. a couple of times per year for a smaller cloud).
There is no clear commitment from Amazon on Windows 2008 R2 support. I think they're working on it, but getting Windows 2008 support took years. Personally, I would not consider a supplier with this track record for something as critical as AD. If Amazon wants to see larger Windows deployments on EC2 they must IMHO make a public and binding commitment to supporting Windows in a timely manner...
The problems above are not exactly dealbreakers; workarounds do exists. But EC2 and AD and Windows -- it doesn't look like a good fit IMHO.
Edit 2011: Updated wording to reflect that Amazon does have Win 2008 support on EC2 now, but still no Win 2008 R2.
Edit March 2011: As @natacado points out, Amazon has just announced support for Win 2008 R2. Given this, I might soften my stance on Windows @ AWS somewhat -- at least now all shipping Windows server OS's are supported; and there isn't a new Windows server release on the immediate horizon. But, it's still not a great track record for Amazon's Windows support IMHO.