Can arbitrary code run in a server if someone's know just the MySQL password?

[Νίκος]

Tim delaney said:

"Because there's no chance with the brilliance you display that there 
could be any possibility of login details being kept in plaintext in 
your database.

And of course your database is so well locked down that no attacker with 
a login to it could then execute arbitrary code on your system.

And there's also zero chance that your personal account login details 
are also available in plaintext somewhere that you're unaware of."
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Is it possible for someone that knows the MYSQL password of a server to 
run arbitrary code on a linux server?

Okey he uses the password and he gain access to the databases, then 
what? MySQL is a database server how can he run run arbitrary shell 
commands by using MySQL?

If yes, can you give an example please?

Also, is there a chance for my account's password to be retrieved on 
some why due to MySQL access or perhaps by utilizing my own python code?

I'm just trying to figure out how the upload of that .html file happened 
to '/home/nikos/public_html'. I need a theory and Zero Piraeus to answer 
too.

Please, serious replies only, i won't answer to ironic comments or jokes.