By the following ways, you can detect that MySQL is already installed or not.
Firstly, If there is no firewall in between, you may check to see if port 3306 is responding as the MySQL Server uses port 3306 by default.
Secondly, it is very possible to have multiple installs of the MySQL on a server without conflict, so done correctly, you won't trash any other MySQL installs. You can simply put all files at another location (your program's folder) and write the my.ini/my.cnf file on the fly, changing the datadir and other options for it to work wherever your program will be located.
Thirdly, you can also use sockets or named pipes instead of TCP/IP to ensure you won't block any port or mess with the network, starting your server without networking support.
Further, you have to figure out if you use PHP if so you must check to see if it is installed as well, and compiled with MySQL support.