Yes, I would say you should upgrade to WP 3.1 instead of importing content in WP 3.1
Like Ian said, you should do an incremental upgrade. I have seen the upgrade working from 2.2.1 to 3.1 directly (Check this tweet)
But lets say you should download and over write 2.3 files over your installation. BRowse in your dashboard, it will ask you to upgrade database, do so.
Then finally overwrite 3.1 files and again upgrade database when you are asked in the dashboard.
and make sure you do a backup before doing anything else, so you can revert back to this state if needed.
Edit: Disable all your plugins before attempting to upgrade. Its very likely to create issues in your case. You don't want to be stuck in between. And I can't stress enough, backup before you do anything.