Not really; the fact that the currency is anonymous doesn't make the loans anonymous. The lender cares that someone is on the hook for the payment being made, they don't care if that person is the person to whom the cash loaned is actually transferred or the person from whom the payments will, in fact, be transferred.
Of course, to establish credit worthiness and get attractive loan terms when the currency itself is anonymous -- whether its paper dollars or Bitcoins -- people are probably going to have to engage in transactions that are recorded and verifiable by the people who they want to trust them (either directly or through trusted third parties), mitigating the benefit of any anonymity inherent in the underlying currency system.
And, loan terms aside, if you want to take out loans whose enforcement relies on the compulsory powers of the states rather than the compulsory powers of lenders who act outside of the rules imposed by the state, you probably need to adopt some kind of protocol that allows you to prove in court that a loan agreement was made with particular terms by a particular lender and borrower and that repayments of specific amounts were made on that loan, which, again, will require sacrificing some of the anonymity inherent in the underlying monetary system.
I would think, even more than that, loans would have issues in an anonymous system.