I know some customers successfully upgraded from CMS6/R2SP2 to Commerce 9. From Commerce 9 to Commerce 11 is a fairly easy task.

I'd say it's not easy or small task, and how much works needed depend on how much you customized your solution. It's definitely doable but without knowledge about your solutions, I'd say prepare for some challenges.

It might be easier if you try to upgrade in small steps - back up, upgrade to next major version, fix all the issues, make sure the sites work well, then repeat. Yes it'll take longer time, but it would help if something goes wrong and you have to go back and do something again. 

I wrote a blog long time ago about upgrading EPiServer Commerce 1 R2 SP1 to EPiServer Commerce 7.5 and the things I encountered.... 

Are there plans to make large changes to the site's functionality?

If so it might be worth considering if building a new site with the latest versions and just migrate in the actual data from the old solution won't be cheaper.

If commerce data is located in another system writing a new import could prove simpler than migrating it through all the versions.

Not sure I agree with Erik. The data transformation over versions are mostly for catalog, and for R2SP2 there was no version (or even 7.5, if they don't care about versioning at all), it's can be as simple as just exporting the catalog and reimporting after everything is done. 

I've been involved in a number of 6 -> 9+ upgrades and I'd say it's a major major ++ upgrade, depending on which features yo use though. For example converting from composer to blocks can take some time if you're not lucky with the migration tool. The old asset system, and vpp-based media, has been replaced. Promotion engine rewritten. .NET framework version. Lots of API changes. Strongly types content types introduced. WWF replaced. Routing changes. Obsolete addons. Also you'll need to do the upgrade in multiple version steps. We've had some annoying issues with deployment manager, ps scripts that failed, sql sp's that wheren't updated and some other things I can't remember.

In the last couple of upgrade projects we've rewritten the sites and migrated the data. If you're running WebForms you'd probably want to convert to MVC anyway :)