Yes, the synchronisation shouldn't remove data from either machine (unless it's replicated on both). Nothwithstanding my assurance, you should still backup your Axim first. On reflection, you could backup to your home PC as (presumably) you won't be deleting the data off of that either
Think about the synchronisation process for a second: say that you are at a business meeting and exchange contact details with a client. You input the e-card into your Contacts database on your Axim and, when you get home and sync, your client appears on your home PC. This is how people can sync with more than one machine.