Given that your relationship is fairly new, the Home Office could have doubts about it's authenticity. However if you have submitted your certificate of approval applications, all you can really do is wait for the outcome.
If the Home Office have any doubts, it is likely to be on the basis that they may try and suggest that she is simply marrying you to stay in the country. However as long as you can show that you have a genuine relationship (they may request further relationship evidence from you in terms of affidavits or statements of support from friends and family), you should be fine. The CoA will obviously not give her permission to remain here, if it is granted all it will do is allow you to marry. She will then have to apply for a spouses visa before the expiry of her current student visa.
I hope this answers your question in which case please Accept. If you require anything further, please ask.
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