Growing the disk in VMware will not do what your expecting. Expanding the drive will grow the size of the disk, BUT the partitions on the disk don't grow with it.
If your system is using LVM, adding the new space and growing the file system is fairly easy.
- grow the drive in vmware
- create a new LVM partition in the new space
- add it to the LVM volume group
- add space to the logical volume
- expand the file system.
If you are not using LVM your going to have to figure out how to expand the partition without losing data while the server is running. Not something I recommend doing. My recently re-installed DB server will back me up on that. :-)
No matter what the setup, your playing with your server's disks and file systems while it's live. Things can go wrong, make sure you have a working backup ready.