No, you don't need to uninstall anything. Just go ahead with the reinstallation.
Let me explain what happens with the MySQL gone away message. When you install the component Joomla! will first copy the files and finally will run the SQL commands. If the file copying takes too long (namely: more than MySQL's timeout limit) then the database connection is closed and when Joomla! tries to run the SQL commands you get the error message and the installation fails. On a decent server the file copying takes a little under 1 second. On a crowded, slow server it may take a lot of time. If it takes more than 60 seconds on your server you'll definitely have a problem. There's no much you can do apart from going to a new, speedier host :(
Nicholas K. Dionysopoulos
Lead Developer and Director
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