Can an unbaptized person receive the sacrament of the sick?

An unbaptized person in our RCIA class is about to undergo a very risky surgery. Can they receive the sacrament of the sick? She has been declared a Catechumen already so we know that should something go wrong she would be considered baptized. However, if she is able to get the sacrament of the sick prior to her surgery, could she still be baptized at Easter?

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