I would check this page out. It talks about file permissions in depth.
But to answer your question directly, no:
The super user "root" has the ability to access any file on the system.
In your example for instance if the file is owned by say
bob and the group owner was also
bob, then you would see something like this:
-r--r-xrw-. 1 bob bob 8 Jan 29 18:39 test.file
The 3rd bit group the (rw) would also apply to root, as root being part of the
others group. If you tried to edit that file as root you would see that you have no problem doing so.
But to test your theory even more, if the file was owned by root:
-r--r-xrw-. 1 root root 8 Jan 29 18:40 test.file
And you again went to edit the file, you would see that you still have no problem editing it.
Finally if you did the extreme:
chmod 000 test.file
ls -lh test.file
----------. 1 root root 8 Jan 29 18:41 test.file
And you went again to edit the file you would see (at least in vi/vim)
"test.file" [readonly]. But you can still edit the file and force save it with
Testing @Stéphane Chazelas claim with a shell script file:
echo "I'm alive! Thanks root!"
[root ~]# ls -lh test.sh
----------. 1 atgadmin atgadmin 31 Jan 30 10:59 test.sh
[root ~]# ./test.sh
-bash: ./test.sh: Permission denied
[root ~]# sh test.sh
I'm alive! Thanks root!
@Shadur already said it so I'm just going to quote instead of restating it:
Note: The execution bit is checked for existence, not whether it's applicable to root.