It can be some problems. Read more at this link: http://tedgustaf.com/en/blog/2012/4/EPiServer-CMS-6R2-general-hotfix-up-to-version-501/

But that is not my problem.
How to upgrade the running site I know how to do. You have to run the database-script also.

But the problem is that I can't find any documentation saying that the Scheduler will run as normal on first version of EPiServer 6 sites on the same server. I can find documentations saying that I have to upgrade all R2-sites on the same server..

As you know, the patch updates both the database schema and the scheduler.exe. Out of curiosity, I reflected the scheduler.exe in 502 and compared it with the one in earlier versions, and it seems there are improvements in error handling. Nothing that suggests that a "502 scheduler" couldn't work with a CMS6 (R1) site.

Assuming that your R1 and R2 sites have different databases, I can't see any problems in patching the R2 sites to 502 while maintaining functionality for your R1 sites, using the new scheduler.exe.

(As a sidenote, the scheduler between R1 and R2 seems to be exactly the same.)

The upgrade is done and I can say that it works without any problem with the earlier versions on the same server. So all EPiServer 5 and 6 (release 1) works.