Hi,
This is very hard to say since we do not have any details about your project. It depends on the customizations you made and other things. Upgrading a default installation from 5.5R2 to v6 takes 2-3 minutes. However there are clients who were upgrading several hours.
But, they did it this way, which is also recommended:
The downloaded the actual copy of the live site and upgraded it on some dev machine and checked if everything is working fine. If not, they fixed the issues and wrote them down. Then, if it is possible, they uploaded the upgraded CMS files to the live server - so the downtime was only the time when uploading new files. If there were made any changes on the live - they already practiced the upgrade, what to expect and how to fix it and then upgraded the live site directly.
However, if you are still not sure, you can use the
Upgrade audit package we offer to our clients.
Best regards,
Juraj Ondrus