Since you are on SP2, then yes.
This has been asked before:
https://stackoverflow.com/questions/3347722/can-i-run-net-4-0-web-applications-on-windows-server-2003
It points to an article here:
http://johan.driessen.se/posts/getting-an-asp.net-4-application-to-work-on-iis6
Also the Microsoft page for the .net 4 framework installer http://www.microsoft.com/en-gb/download/details.aspx?id=17718 shows the requirements to be:
Supported Operating System
Windows 7, Windows 7 Service Pack 1, Windows Server 2003 Service Pack
2, Windows Server 2008, Windows Server 2008 R2, Windows Server 2008 R2
SP1, Windows Vista Service Pack 1, Windows XP Service Pack 3 •Windows
XP SP3 •Windows Server 2003 SP2 •Windows Vista SP1 or later •Windows
Server 2008 (not supported on Server Core Role) •Windows 7 •Windows
Server 2008 R2 (not supported on Server Core Role) •Windows 7 SP1
•Windows Server 2008 R2 SP1 •
Supported Architectures:
•x86 •x64 •ia64
(some features are not supported on ia64 for example, WPF)
Hardware Requirements:
•Recommended Minimum: Pentium 1 GHz or higher with 512
MB RAM or more •Minimum disk space: •x86 – 850 MB •x64 – 2 GB
•
Prerequisites:
•Windows Installer 3.1 or later •Internet Explorer
5.01 or later