You certainly can but yes, you will need an applet that runs a non native
file picker allowing more than one file or a folder to be selected from the
browser....etc etc The user will have to agree to the applet accessing their
local hard drive and of course be running a suitable browser.
(This shouldnt be a big deal if they really want to use such a feature.. and
you explain to them what is going on)
I do belive you can even gets the applets signed through verisign should you
go that far.
As for builing your own applet.
Since this is file uploading and rather complex most likely you'll need to
buy one and they are rather expensive.
Building one on your own would probably be a nightmare and there would
certainly be bugs with various things. Browser versions/mac issues etc etc
This page I found mentions the multiple file upload issue and also links to
a couple commerical products that handle it.
http://www.cjwsoft.com/aspgallery/pro_add_ons_safileup_multi.asp