I want to restore SharePoint 2007 from backup files (taken through Central Administration Site) with fresh installations of database and application server. Is it possible or not??
WHAT TO RESTORE ?
Firstly, we need to check, what all we need to restore.
When you do a fresh installation of database and application server, you will require to restore the content dbs, configuration db for Central Admin, the configuration setting changes in the Farm, like IIS settings, Email settings, Content Deployment settings,etc and other customizations made to web.config and web part deployments.
Features supported by Central Admin Backup
Now, when you say, backup taken from Central Administration, reading this msdn article helps you to identify what features would not be backed up. We can conclude that any configuration settings or Customizations won't be backed up.
Restoring only works with a fully stopped farm
And a backup of the configuration database and Central Administration content database should only be taken from a fully stopped farm for proper restore. If the configuration and Central Administration content databases of a farm become unsynchronized, you must re-create both databases by using the SharePoint Products and Technologies Configuration Wizard or Psconfig command-line tool.
You can use farm-level backups of a running farm taken with System Center Data Protection Manager to recover an entire farm, including the configuration database and Central Administration content database. Full Details here.
Also check out all other options for a successful Farm backup and restore.