Can I run geeklog under my temporary domain given to me by my new host:
visitwoodhaven.netfirms.com

or do I have to wait for my domain to fully propagate to the new server before this script runs?

You can run it on any fully qualified domain.
If the domain changes you need to change the URL in config.php as well as any other aspects to the site that you include the domain in... possibly using FCKeditor for images uploaded by FCKeditor which use a full url to pick up an image rather than the Geeklog standard of [siteurl] those are the only problems I can see, i have switched the domain of a few sites so it shoudl be OK. I would say as long as the site is not to complex and there is not to much custom code or plugins reliant on a full URL then this will be fine.

There is just one problem with cpanel`s temporary domains which have something like example.com/~user1. I think they work with HTML but not with dynamic systems but this is rather a cpanel problem.