You should've fired up Bing on your shiny new SP3 and searched something like, oh I don't know, "Sony Vegas 12 requirements"?
http://www.sony.co.uk/pro/product/broadcast-products-creative-software/vegas-pro-12/specifications/
Minimum requirements
- Microsoft
Windows Vista
64-bit SP2, or Windows 7 64-bit
- 2 GHz processor (multicore or multiprocessor CPU recommended for HD or stereoscopic 3D)
- 500 MB hard-disk space for program installation
- 4 GB RAM (8 GB recommended)
- OpenCL
-supported NVIDIA
, AMD/ATI
, or Intel
GPU with 512MB memory or more, for GPU-accelerated video processing and rendering
- IEEE-1394DV card (for DV and HDV capture and print-to-tape)
- USB 2.0 connection (for importing from AVCHD, XDCAM EX, NXCAM, or DVD camcorders)
- Windows-compatible sound card
- DVD-ROM drive (for installation from a DVD only)
- Supported CD-recordable drive(for CD burning only)
- Supported DVD-recordable drive (for DVD burning only)
- Supported BD-R/-RE drive (for Blu-ray Disc
burning only)
- Microsoft .NET Framework 3.51 (included on application disc)
- Apple
QuickTime
7.1.6 or later for reading and writing QuickTime files
- Internet connection (for GracenoteMusicID Service)
So yes it will run, but it may take longer to render.