Yes i am sure the bank who lent her the money would be OK with this.
Becareful, they have very tight conditions on what they will pay out for, often making them a waste of time. But it depends on her circumstances.
For example, if she took out insurance now and got made redundant i am sure there will be a clause that you had to have paid 6 month (Example only could be more or less) contribution.
Also, some of these policies will only cover repayments for a certain amount of time. So, if the loan is for a small amount, it may not be worth her while.
In addition to that, does she have sick pay in her job/is she likely to be made redundant? Is she self employed - many don't pay out to self-employed people.