Since Java 7 isnt yet as popular as Java 6 I was wondering if I could use some stuff like WebView in latest update of Java 6 JRE out of the box, without having users download JavaFX on their system.
No, Java 6 will not run JavaFX 2 out of the box.
If developing a new JavaFX application today I recommend targeting a minimum version of Java Runtime 7u9 for the following reasons.
Java Runtime 6 and JavaFX for Java Runtime 6 are due to cease public distribution in February of 2013.
Java Runtime for JavaFX only works with a separate download installed - this could be confusing to users of your application.
The JavaFX for Java 6 Runtime only works on Windows and, due to Oracle's Java Runtime autoupdate for Windows, Java on Windows machines is usually at the latest public version.
If you instead target your application to a minimum of JavaFX 2.2 and Java Runtime 7u6, then your application will run a wider variety of platforms (Windows, Mac, Linux) and have more deployment options (e.g. self-contained applications).