Hello, I hope the following assists you.
Firstly you are correct, a turbo fault would not cause the battery to go flat. I would have the cause of this investigated first as it may or may not be related to the noise.
The alternator on this engine isn't driven directly by the fan belt, there is a pulley with a one way clutch and rubber cushion plate that is driven by the fan belt, this is bolted to the alternator pulley and drives it. The clutch and rubber in this pulley do fail, when you look at them with the engine running it can appear OK but on further inspection the pulley can be turning where driven by the fan belt but the alternator doesn't turn obviously causing a flat battery, it also makes a noise as the damaged parts spin against each other.
The garage should be able to check the charge rate of the alternator, with the heated rear screen on and the headlamps it should be producing around 13.5 volts, usually higher on this model.
There are a couple of turbo pipes that split on this engine, the pipe from the intercooler to inlet manifold splits near the joint to the manifold and the pipe from the turbo to the intercooler can split near the gearbox. In both cases there is usually a sign of oil around the pipe and if you rev the engine you can hear a high pitched whistle as the air escapes from the split under boost pressure. The noise is usually louder on acceleration and disappears when the throttle is released.
As I said at the beginning a turbo fault won't flatten the battery so get to the bottom of that problem first.
Let me know if I can advise further and I'll reply as soon as I'm able to.