How do I prevent the "Updating Steam" dialog from showing up
Solution 1:
Yes, there is a way!
In order to hide the update dialog, simply run Steam with the -silent command line option.
As usual, any other dialogs (such as going into offline mode due to a lack of internet connection or a missing Steam Service warning) will appear. Those cannot be suppressed.
If you do not want Steam to verify its files (check integrety), run steam with the -noverifyfiles command line option.
You can read the list of command-line options here.