Is it possible to upload a file of size 300+ MB on shared hosting such as host gator ?
If you mean via php, the hostgator limit is 64M as you can see in your cpanel in the section "Software/Services" and then look at "php.ini QuickConfig".
If you mean via ftp, there's no limit.
If the PHP.ini upload_max_filesize is set to have a limit of 300MB or more then, yes. You need to ask the hosting company what their limits are set at before signing up for hosting with them.