In theory yes the AMD driver should work, but it also has this to say in the release notes,
AMD Mobility Product Family Compatibility
AMD Catalyst™ Mobility is a notebook reference graphics driver with limited support for system vendor specific features. When used with Windows Vista or Windows 7, users may have unwanted experiences.
The Installation Verification Software will prevent driver download on certain notebook products. This is to protect against the installing of drivers that may disable features or functionality provided by the system manufacturer. If unwanted experiences occur using AMD Catalyst™ Mobility, it is recommended to revert back to the driver provided by your system vendor for your specific platform. Please contact your system vendor for the most recent drivers for your notebook.
If even the Dell driver is causing it, I would start with doing a system restore to before you uninstalled the driver the first time. If that solves the BSOD problem then leave well enough alone or only get an updated driver from Dell. If it doesn't fix it I would then contact Dell and see what they have to say.