I suspect that it won't, but it won't hurt to try. The installer should error out if it isn't happy with your hardware configuration.
That computer hardware isn't tested for InDesign to run successfully at given stressed conditions. Even if it installs and launches on your computer, there is no guarantee that all functions will work as expected. Please check this document to ensure your system requirements match before using InDesign: http://www.adobe.com/products/indesign/tech-specs.html