After Effects project files are cross-platform compatible. Things to watch out for are that file paths are valid, and that fonts and plug-ins are installed and working. You should open the project on a Windows machine to check for any errors, especially with fonts. Some fonts may have different names between platforms.
When using Collect Files, the source file paths are set relative to the project so this is usually not a problem. But you must make sure that the output file paths are also valid; using the Change Render Output To option in the Collect Files dialog can help with this.
More detail here:
After Effects Help | Automated rendering and network rendering