I haven't used the mentioned os uninstaller.

As for partitions changing numbers, that will probably happen, but all recent versions of ubuntu use UUIDs and not the traditional /dev/sdXY notation, and the same applies to grub2.

So, even if the partitions change numbers the system should still work fine because it finds the partition by UUID which is the same unless you format a partition. By formatting it gets new UUID.

In worst case, you can always edit fstab from live mode.

Open fstab and check the above mentioned. If you see something like UUID=<string> and not /dev/sdaX then it's using UUIDs and you have nothing to worry about partition numbers.