However, both I and a colleague have experienced issues doing that.
On his machine (XP) he is unable to launch ArcCatalog 9.3.1 after installing ArcGIS Explorer 1500. ArcMap 9.3.1 launches fine. Uninstalling ArcGIS Explorer 1500 leads to ArcCatalog 9.3.1 being launchable again.
On my machine (Vista SP2) I have no problem launching ArcCatalog 9.3.1 with ArcGIS Explorer 1500 installed. However, I am unable to switch ArcGIS Explorer (with just the default Basemap) from 3D to 2D view. On my other, and much lower spec-ed Vista SP2 machine which has ArcGIS Desktop 10 and ArcGIS Explorer 1500 installed switching ArcGIS Explorer from 2D to 3D works fine.
It's only a suspicion but are ArcGIS Explorer 1500 and ArcGIS Desktop 9.3.1 not as sociable as the System Requirements URL above suggests?
Despite my efforts, I have been unable to reproduce the error you're seeing on your 64-bit XP machine: ArcCatalog and ArcMap failing to launch once ArcGIS Explorer 1500 is installed. I tried to mimic your system configuration, but was still unable to recreate the problem.
Here are some general "good practice" items to keep in mind when installing ArcGIS Explorer: 1) Stop all of your ArcGIS Services (eg. ArcGIS Server Object Manager) before installing Explorer. 2) Allow all installations to complete without interruption. The Explorer installation may appear frozen at times, but it's important to allow it to complete. 3) Review ArcGIS Explorer Knowledge Base Articles here: http://resources.arcgis.com/content/kbase?p=116&fa=tree
If the problem persists, I recommend contacting ESRI Support.
Thank you very much for the information you've provided and your feedback.