As @Ed__Jobe said, the code itself would convert automatically (i.e. syntax-wise), it is not guaranteed that the code for 32-bit VBA would pass the compiling either because of being 64-bit VBA, or because of being in different computer.
If the code uses some components only available for 32-bit VBA (such as any controls which is not AutoCAD VBA built-in ones), most likely there is no 64-bit replacing counterparts, thus the code would not compile and would not work. You need to either re-write the code, or find replacing components (which would result in code re-write more or less anyway).
If the code uses some components which is not available in this newer computer, the code would also not compile (such as if the code has references to MS Excel type library, but the computer does not have Excel installed).
So, in either case, if the code does not compile, you can open "menu->tools->References...", and in the "References" dialog box, look for something flagged as "Missing...". Then decide what it is and what to do. If it is something missing and not replaceable (especially 32-bit specific controls), then you'll need to rewrite the code, or give it up and move on to newer/other technologies (Acad .NET API, LISP...).