If you set it to download a specific path/directory (on the remote site), it will.
You might then want to set FlashFXP up to "skip" existing files with the same date/time, unless it's only one file that gets updated daily - then it should "overwrite" instead.
So all in all, it depends on what's in the folder you want to download from.
You could also just do it in another way, by selecting a specific file from a date or something, by using something like:
"<full path to flashfxp.exe>" -go -c2 -download <sitename> -remotepath="<full filepath on remote site>" -localpath="<full filepath on local computer>"
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