Anna,
No, they can not. A baptized Catholic must marry in the Church for it to be a valid marriage.
You might need to clarify in your mind the difference between the terms valid and sacramental.
The first scenario you mentioned, (a Catholic and a non-baptized person getting married in the Catholic Church,) would be a valid natural marriage. It would be recognized by the Church, but would not have the supernatural dynamic that a marriage of two baptized people would enter in to.
The second scenario you mentioned, (a Catholic and a non-baptized person entering into a civil marriage), would be neither valid nor sacramental, if one of the parties is Catholic.
Paul
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