No. First you would need to partition your hard drive devoting your current partition to Mavericks, then installing Mountain Lion on the other partition. However, you need a copy of the Mountain Lion installer or you will have to re-download Mountain Lion if it was purchased on the App Store.
If Mountain Lion was pre-installed then you need to do this:
Install Mavericks, Lion/Mountain Lion on a New HDD/SDD
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
Boot to the Internet Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND-OPTION- R keys until a globe appears on the screen. Wait patiently - 15-20 minutes - until the Recovery main menu appears.
Reinstall Lion/Mountain Lion. Mavericks: Select Reinstall Lion/Mountain Lion, Mavericks and click on the Install button. Be sure to select the correct drive to use if you have more than one.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.
This will reinstall the original version of OS X installed on the computer which would be Lion or Mountain Lion depending on which was pre-installed at purchase.