That depends on the code. Perl code can be written quite portably. Here are some issues you might face:

• ActivePerl may come bundled with some non-core modules that aren't included with Strawberry Perl. This would only be an issue if your program uses those modules. However, Strawberry Perl is designed to make module installation just about as simple (and standards-conformant) as possible. So you may need to install a module or two to get it working. But that's only if the Perl code happens to use a non-core module that ActivePerl bundles, and that Strawberry Perl doesn't.
• It's possible that your code includes some pre-compiled XS code that has been compiled for use with Active Perl (ie, for use with a Perl compiled with a Microsoft compiler). That extension code wouldn't be binary compatible with Strawberry Perl. However, common practice is to distribute modules as source-code that is compiled at install time. So unless you've got something fairly non-standard, this should also be a non-issue.

But here's the really great secret. You yourself can download Strawberry Perl for free, and you yourself can test the code to verify that it will work as expected. Installing Strawberry Perl takes just a few minutes. And you are the only one so far in this thread who has any idea what the code you intend to run looks like, so you're the only one who can render a definitive answer to your question.