No, of course this is not what context processors are for. They are for, er, processing the context. The only thing they can do is add items to the template context before it is rendered. They have no control at all over the response - the template that is being rendered may not even be part of the response (think of an email being created from a template within a view, but the response is rendered from a separate 'confirmation' template).
Rather than putting the form in a context processor, I would use a template tag that only renders the original form. The form itself should post to a specific view, so that the POST is processed there instead of in the context processor.
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DR.