Thanks for your question!
You can programmatically move the caret to the last position in document. Thus the viewport will be moved too and you will get the desired effect.
Use the following code:
We have plans for adding an API for programmatically scrolling the view port of RadRichTextBox but I cannot state whether it will be available sooner than our next official release.
Please do not hesitate to contact us if you need any further assistance.