On our server we are running GNU Libc 2.11 and we want to update MySQL 5.1 to 5.6.
Just to be sure that this won't fail i'm looking for information of if this can be done with the current Glibc version.
Anyone? :)
Yes.
Linux distributions use packages to install or uninstall software. These are similar things as the .msi on windows, but they contain dependency informations, too: every package contains which other packages it needs, and at least (or at most) which versions.
There are multiple package management systems (rpm and dpkg are the most common), it depends on the distro which is used by you, but they are the same from this aspect.
If you install mysql 5.6, it will either upgrade the libc as well (and so, all other programs which need a newer libc), or it won't be installable. Or it will simply work (if they are compatible).
A bigger danger for the mysql upgrades isn't the possibility of the incompatibility with the libc, but the incompatibility of the mysql databases between the mysql versions. I.e. your mysql-5.6 will perfectly work with the libc, but it will have troubles to use the databases files he got from the 5.1.
It is highly suggested to make a backup from your mysql directories (/var/lib/mysql) and configurations (/etc/mysql), and even a dump (mysqldump --all).