I have a a domain and hosting reseller anotherkitty.com that utilizes the SAME hosting services/support etc as Godaddy and used shared but deluxe hosting and have very heavy graphic files and this worked AMAZINGLY, Loved it. I am a Joomla person as well and it was quicker than Akeeba (which I also Love) but Joomla is a little thicker.
So Short answer, yes I talk too much… You should NOT have any time out issues, however if you do give them a call.