You will only be able to use the additional user pictures for the time that you choose to pay for. When your add-on time expires, which is independent of your paid account expiration time, ...
Later on the next paragraph, it states:
You can only purchase user picture add-on time for the length of your paid account. If your paid account expires before your add-on time expires, your userpics will be inactivated, but they will be available again when you choose to pay for your account again.
I think a better wording would be:
Your additional user pictures will only be available for the length of time you purchase and as long as your account remains a paid account.
If your paid account expires before the end of the additional user picture time you purchased, your additional user pictures will be inactivated but remain on the LiveJournal server for six months. If your account does not return to paid status within six months, your additional user pictures will be removed from the server, and you will need to re-upload them if you upgrade your account after this six-month period.
When either your paid account or your additional user picture time expires, the system will deactivate enough of your least-used user pictures to bring you to your account's usual limit in accordance with the information at http://www.livejournal.com/support/faqbrowse.bml?faqid=46.
Updated (2004-02-10 // 16:30 ET): The above block has been updated with better wording.