Yes. It has a built in browser. To download from "My downloads" with your iPhone, iPad, or whatever using Goodreader:
1) click on the "Web Documents" tab on the right
2) click on "Browse the Web"
3) login into your "My Download" section of this website
4) click on the item you want to download and "Follow Link" in the grey popup
5) Here there are three ways:
a) wait 5 seconds and you'll get a purple popup error say "Frame Error" -ignore that
b) click on the "click here" and get the purple popup error saying "Frame Error" - ignore that
c) copy the "click here" link and go back to Goodreader - go to step 6b
6) Check your "Downloads" folder in the top left and see if the file downloaded (should be a ZIP)
a) If not then and go under the tab "Resent Downloads"; there you will see the failed download, click on the retry button and it should work
b) If that didn't work copy and paste the url into the "Enter Url" under the "Web Downloads" tab
7) You should have a ZIP file in your "Downloads" folder in the top left of Goodreader now
8) Go into that folder and click + hold on the file.
9) Confirm that you want to unzip the file
10) The PDF should now be there now.
11) I like to remove the ZIP and rename the PDF (click + hold) on the file to do an operation
12) You can now view the PDF in whatever reader you want on your device ... click + hold and you can "Open In..."