I believe you do need to copy them, but an easy check would be not to once and see what happens. From MSDN, they're only used to find the right assembly when serving a request on that page/control/master:
.compiled Files:
For executable files in an ASP.NET Web application, the compiler assemblies and files with the .compiled file name extension. The assembly name is generated by the compiler. The .compiled file does not contain executable code. Instead, it contains only the information that ASP.NET needs to find the appropriate assembly.
After the precompiled application is deployed, ASP.NET uses the assemblies in the Bin folder to process requests. The precompilation output includes .aspx or .asmx files as placeholders for pages. The placeholder files contain no code. They exist only to provide a way to invoke ASP.NET for a specific page request and so that file permissions can be set to restrict access to the pages.