If you create a character style to base another character style on then - theoretically - when you change the base character style the styles based on that base style should change automatically.
However, and here's why I said "theoretically" near the start, some changes aren't carried through automatically.
For example, if you start with "Arial Regular" in the base style and "Arial Bold" in the derived style and then change the font in the base style to "Minion", Scribus won't automatically change the font in the derived style. You need to change that yourself. Scribus isn't clever enough to check the new font to see if it has a bold variant and automatically make the switch. This usually isn't a huge problem and making the change is way quicker than manually formatting stuff but it needs to be taken into account.
Although this is an old message, it deserves clarification.
This supposed problem of inheritance prefaced by "theoretical" is no problem at all; it is exactly how inheritance should work.
First, at least in version 1.4.6, when you define a new style (the CHILD) and base it on another style (the PARENT), the CHILD is displayed indented under the PARENT in the Style Manager
PARENT: The style that is the base for other styles.
CHILD: The style that uses the PARENT style as its base.
If you make no changes at all to the CHILD style, then every change you make to the PARENT style is inherited (and therefore implemented) by the CHILD style. So the result of applying either the PARENT style or the CHILD style are exactly the same.
There are two major points of having a CHILD style--it avoids copying a lot of the style settings into a new style; it enables the PARENT and CHILD styles to have some style settings that are the same that can be changed in both by changing the setting in the parent, and some other style settings in the CHILD that when changed, affect only the CHILD style and not the PARENT style. Unfortunately, Scribus does not have any method to distinguish in the CHILD settings which are inherited and which have been changed in the CHILD; you must flip back-and-forth between the PARENT and CHILD (or else write down the settings of one of them) to determine what is changed in the CHILD.

Example
PARENT You define BodyText as family: Times New Roman, size:12, fill color:black, style:regular
CHILD You define a new style named Captions. When you start to edit Captions settings, you find they are exactly like the parent settings, as they should be. But you want a sans serif font, so you change the family setting to Helvetica. When you viewed samples of BodyText and Captions, you decided Captions size is a little bit too big, so you change the size to 10. So now Captions is family:Helvetica, size:10, fill color:black, style:regular.
At some later time, you decide that you want BodyText to be blue, so you edit its fill color to blue, and both BodyText and Captions to have a size of 11, so you edit the BodyText size to 11. So what happens? The color of both fonts is now blue, because Captions inherits its color from its PARENT, BodyText. But you did not want Captions to be blue, you wanted it to remain black. So you now must edit Captions to fill color: black.
And what happened when you made that font size 11 in BodyText? Notice that BodyText is 11 as desired, but Captions did not change. This is because you previously set Captions size 10, so it no longer inherits from BodyText. Therefore, you must edit Captions to size:11.