Yes, it can, especially if you are using Reader 8 or 9. There were some issues with earlier reader versions that required the positive confirmation of the Reader Extensions credential with the certificate revocation list (CRL), which required that it had to go out to the web to fetch the CRL.
Depending on how deep you want your testing methodology to go, I'd take a virgin windows machine that does not even have reader installed, download or otherwise transfer the RE installer and your form and take it offline. Then install Reader and open your form. It should open with the additional rights with no problem.
But the bottom line is that it is designed to work for your use case.