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Yes, if she is the one who pays the the insurance bill (premium). She will get a statement from the hospital on the procedure, and a cost and it will tell her how much she owes. Sometimes this is called a statement and a Certificate of Benefits or Certificate of Coverage.
If you are trying to avoid having your mother see what happened at the hospital, you might have to do one of the following: 1) ask the hospital billing department if they can bill you directly though you are on your mom's coverage for privacy and financial reasons. Hospitals are very tuned in to patient privacy and they will probably accomodate you. 2) Or you will have to intercept the statement at your mom's house before she sees it.