My Twitter favourites were all created in the past, so to preserve the dates I need to.
And the answer appears to be: yes I can, and they get sorted correctly for public display, but on the dashboard they appear in the order created.
Edit (April 8th 2011):
This post is getting a lot of views via Google, from people who’ve searched for things like “backdate posts tumblr”. So here’s how to do it:
When creating or editing the post, simply enter a post date which is in the past. The post then gets sorted on your Tumblr page as though it had been created then.
What I haven’t tested (yet; maybe I will) is whether there’s a limit to how far back the date can go.
Further edit (Jan 24th 2012)