We are about to post an app that use UDID. We plan to remove this access due to the mess that Apple does around this identifier access. But we plan it for the next release.
Because I'm afraid of failing my review, I would know your experience :
Have you post an application these last weeks that use UDID? Does Apple began to reject that kind of apps?
[UPDATE]
Just saw this http://techcrunch.com/2012/03/24/apple-udids/
In my humble opinion you should implement your own method for generating a UDID now. It is not that hard and there are plenty of good references around the web.
Thing about how much more work it will be required once UDID is removed from the SDK and you need to work out a migration strategy for your existing users. Definitely not worth the trouble.
In saying all that, I doubt your app will be rejected for using a deprecated method.
Here is a similar SO question in case you're interested Has anyone had their iOS App rejected by Apple for using the devices UDID?