Yes, Buxfer is designed to work even if you can't or don't want to sync your bank accounts.
You can use one of these methods to enter your transactions:
Upload statements: Download statements from your online banking website and upload them to Buxfer.
Read more here.
Manually enter transactions: Manually enter transactions one at a time. While more tedious, this is also
more flexible and allows you to enter future-dated transactions, itemize transactions, etc.