I did the process for deploying my Laravel 4 app yesterday proposed by Sas Sam and did not need to install Composer--but I can see why people would do that, because with ftp, using Filezilla, I ran into the issue that out of over 3000 files, it missed--or rather copied "empty files" for four php files, including one of the major classes of the Illuminate class (RedirectRequests.php), causing the app to throw an error early on.
When I realized that file was empty, I spent several hours in Filezilla examining every file (there are a lot besides php files, but only php files that were empty were causing issues) in the Laravel folder I'd created, cross-referencing them with my local install, to paste code into a total of four "missing" php files, and it seems to be working fine now.
So perhaps doing a linux install of Composer directly on the server and then doing a fresh install of the same version of Laravel might have avoided that, I've been having issues with GoDaddy getting SSH access to my project so elected to just fine-tooth-comb my project, instead. As long as you have all the files up there, properly referenced through the bootstrap.paths and public index.php files, it should work.