Precedence of logical operators versus semicolon

Yes, and you can easily check it yourself:

$ non-existent-command && echo hi ; echo after semicolon
bash: non-existent-command: command not found
after semicolon

In man bash it says:

Commands separated by a ; are executed sequentially; the shell waits for each command to terminate in turn.

commandC will be executed no matter if commandA or commandB fails or succeeds.

Semicolon is just a separator to make commands execute sequentially. The only scenario that I can see where commandC will fail, is if commandA or commandB are exit commands (or any command like return/break/continue/exec (or functions that call those) that forcefully affects the work flow):

Scenario 1: commandA is exit

[root@host ~]# exit && echo "HI"; echo "test"
logout
[user@host ~]$

Scenario 2: commandB is exit

[root@host~]# echo "HI" && exit; echo "test"
HI
logout
[user@host ~]$

tl;dr: Is not that those characters have a precedence. They mean different things. One is a logical operator and the other is a list terminator.

Related Stuff:

• What are the shell's control and redirection operators? This answer gives a good explanation about the bash operators. Quoting a little piece of the answer:

  • ; : Will run one command after another has finished, irrespective of the outcome of the first.

    command1 ; command2
    

    First command1 is run, in the foreground, and once it has finished, command2 will be run.

    A newline that isn't in a string literal or after certain keywords is not equivalent to the semicolon operator. A list of ; delimited simple commands is still a list - as in the shell's parser must still continue to read in the simple commands that follow a ; delimited simple command before executing, whereas a newline can delimit an entire command list - or list of lists. The difference is subtle, but complicated: given the shell has no previous imperative for reading in data following a newline, the newline marks a point where the shell can begin to evaluate the simple commands it has already read in, whereas a ; semi-colon does not.

• Semicolons superfluous at the end of a line in shell scripts?  Quoting the answer:

  Single semicolons at the end of a line are superfluous, since the newline is also a command separator. case specifically needs double semicolons at the end of the last command in each pattern block; see help case for details.

• What's the difference between semicolon and double ampersand &&