I am not satisfied with your answer as the UKBA guidelines below state otherwise. I have highlighted text in bold which state otherwise
3.2. Applications lodged during leave under sections 3C and 3D
While either section 3C or 3D leave is in force, the applicant is not entitled to make
any more applications for variation of leave to enter or remain. So even someone
who marries after making an application to remain as a student cannot, while they
have leave under section 3C, make a fresh application on the basis of the marriage.
On the other hand, it is possible to vary the grounds of an application already made,
even by introducing something completely new. A student application can be varied
so as to include marriage grounds. If an application is varied before a decision is
made, the applicant will be required to complete the necessary prescribed form to
vary his application. If an application is varied post decision, it would be open to the applicant to submit further grounds to be considered at appeal. As a result, there may be little difference in practice between a fresh application and a request to vary an existing application. The distinction is made to ensure that all a person's grounds for wishing to remain in the UK result in one decision and thus one appeal. This 'one-stop ' principle - one application, one decision, one appeal - is essential to the
operation of the appeal process that was introduced in the1999 Act and has been
extended by subsequent Acts.
However section 3C makes a clear distinction between the decision on the
application and the appeal against that decision. Once an application has been
decided it ceases to be an application and there is no longer any application to vary
under section 3C (5). So any new information will fall to be dealt with during the
course of the appeal rather than as a variation of the original application.
When section 3D applies leave has been curtailed or revoked. Thus there is no
application for the variation of leave and the question of whether an application can
be varied or not does not arise.