Only if your Child Style is the same as your Parent Style -- with the exception of CSS Changes or Image Changes.
Example: Take the Default vBulletin, this would be the Parent Style. Then you have a second copy of the Default vBulletin, called Red vBulletin - which is a Child Style of Default vBulletin. Red vBulletin is identical to Default vBulletin, except it's got CSS Changes which have changed its color from default to red -- hence the name.
If I edit the Navbar template on Default vBulletin, the changes will carry over to Red vBulletin, because Red vBulletin uses the same templates as Default vBulletin.
Hope that makes sense.
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