As long as it does not do a lot of 3d rendering, the standard system should be usable. The current recommended requirements for Mechanical Desktop are :
System Requirements
For training (minimum): Intel® Pentium® II or AMD Athlon® based PC with 450MHz processor or better with 128MB RAM
For part modeling: 450MHz or faster processor with 256MB RAM and OpenGL workstation graphics card
For assembly modeling: 600MHz or faster processor with 512MB RAM and OpenGL workstation graphics card
Microsoft® Windows® XP Professional (supported with Mechanical Desktop 6 SP2 and later), Windows 2000 Professional, Windows NT® 4.0 (SP6a or later), Windows 98 SE, or Windows Me
Microsoft Internet Explorer 5.0 or later
Note: Less capable machines (such as Pentium II 300) can run Mechanical Desktop 6, but the results will likely be less than ideal. The use of additional memory and later generation, faster processors will directly improve performance and capacity and are highly recommended. Typical production systems employ a 1GHz or faster processor with 512MB to 1GB RAM and an OpenGL hardware accelerated graphics card.
If it fits that, it should run fine. Mechanical Desktop is more demanding than LDD or plain Mechanical.