It's quite possible. Many people who upgrade then have problems usually had problems before the upgrade. The upgrade merely made them worse. For future reference:
System Upgrade and Installation Procedure
Basic Caveats
1. Disconnect all peripherals except the original mouse and keyboard.
2. Quit all applications if this is not an installation from an Installer DVD.
3. The installation process should not be interrupted. If a power outage or other interruption occurs during installation you may have to erase the hard drive and reinstall from scratch.
4. Once the installation begins do not use the computer in any way except to reply to dialog prompts or to restart when the installation is completed. This is especially critical during the installation stage known as "Optimizing the System."
System Update Procedure
A. Repair hard drive and permissions.
Repairing the Hard Drive and Permissions
Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Installer menu (Utilities menu for Tiger or Leopard.) After DU loads select your OS X volume from the list on the left, click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.
If DU reports errors it cannot fix, then you will need Disk Warrior (4.1 for Leopard) and/or TechTool Pro (4.6.2 for Leopard) to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X. Note that Disk Warrior will not work on Intel Macs.
B. Clone your existing system to an external Firewire drive.
How to Clone Using Restore Option of Disk Utility
1. Open Disk Utility from the Utilities folder.
2. Select the startup or source volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Drag the startup or source volume to the Source entry field.
5. Select the backup or destination volume from the leftside list and drag it to the Destination entry field.
6. Check the box to Erase Destination. Skip this step if you've already formatted the drive.
7. Double-check you got it right, then click on the Restore button.
C. Decide upon an installation option.
You have
three upgrade options. If you use the Upgrade installation option be sure you have repaired the hard drive and permissions first and made your backup. If you choose the
Archive and Install option then you only need to repair the hard drive.
Neither of the above options will erase the disk. Some of your software may not work with a new system. You will need to upgrade those programs. It would be best to do the upgrades to your software before upgrading to the new system version.