It depends on the parent theme and flexibility it includes.
Shouldn’t be a problem as long as you use the correct code.
You can generally modify the output of existing parent theme functions using filters and use action hooks to add new functionality.
I don’t think parent themes with built in options are best for people who want to fully customize their site using a child theme.
2 examples of this would be customizing the Woo Canvas theme which includes a large options panel built in compared to creating a blank child theme to customize the Genesis theme framework.
You’d find it easier to customize a Genesis child theme as opposed to the Canvas theme.
Genesis offer dozens of plugins to add options rather than build them into the theme however you will find problems trying to modify functions added by plugins with Genesis. The simple solution is you can deactivate the plugin and use code instead or load the child themes style sheet after the plugins style sheet.
With Canvas including a heap of built in options, you can’t simply deactivate these options. You can modify the parent theme which isn’t best practice or try and use filters to modify the built in functions if Woo include them.