Do MtGox issue loans?
Not to my knowledge.
If not, why would they ever issue more in redeemable codes than they have in reserve? As far as I know, I can only withdraw codes up to my current balance.
There are a variety of reasons, but those most common is to protect themselves from devaluating currencies.
I was under the impression that MtGox were holding everyone's balance somewhere safely. Is that not the case?
No, you don't stuff money in a mattress unless you're an idiot. If, for example, dollars are losing value, MtGox should hold as little of their reserves in dollars as possible. There's no reason they have to hold your value in the same demomination as you are going to claim it, and that's usually a very foolish thing to do. If Mt. Gox did that, they'd have to charge you a storage fee or eat losses from inactive accounts.
Mt. Gox should hold sufficient value, in some form ,t cover client deposits. Butthey shouldn't hold reserves in any particular currency of store of value unless that particular currency or store of value makes sense for them.