Removal of an old version is best done before installing a new one.
However, you should be able to uninstall the old version, but depending on how the new version was installed, be prepared to have to repair the new version afterwards.
Does the old version still work?
Are you wanting to uninstall to reclaim storage space or just for clean housekeeping?
Just for housekeeping.
The old program is still selectable, but now it requires an activation key.
Activation over the internet to SolidWorks Hq became a requirement with SW2007 SP3.
I would keep the old program around. You never know when you might find something that is broken in a newer version. It's nice to have the old version to see what it is supposed to look like.