It seems that initializing this property chain:
rtbSpellChecker.SpellChecker.Settings.SpellCheckUppercaseWords = true;
causes the DocumentSpellChecker to be replaced by a new instance.
Workaround: Add an additionally registered RadRichTextBoxSpellChecker:
RadRichTextBoxSpellChecker rtbSpellChecker = new RadRichTextBoxSpellChecker();
rtbSpellChecker.SpellChecker.Settings.SpellCheckUppercaseWords = true;
ControlSpellCheckersManager.RegisterControlSpellChecker(rtbSpellChecker);