Will FileZilla resume interrupted downloads?

You can.

A file will remain in the transfer queue if you disconnect the client. When you restart your machine, right click on the file to resume and you will be offered the choice of overwrite or resume (and a couple of others). Choose resume and off you go!

To resume downloading after disconnected, open Filezilla ftp interface, just drag the file from the source to the right side over the one you wanna resume, it will ask to overwrite, select resume and click ok