For that age it should be fine at it's core, but could be having problems at the outer end.
If you hear a whistling sound coming from the alternator, it's not the bearings (test them for play anyway, to make sure), but the brushes and worn out contact on the rotor, the slip rings. The outer slip ring usually wears out pretty fast, while the inner one stays almost like new. That happens because it being on the outer side, very much dust gets to it and it gets caught between the ring and the brush. And that wears the slip ring like a grinder and that's the sound you gonna start to hear from it at one point, like the sound made by a grinder.
Here are some pictures in wich you can see the phenomenon.
I got a new alternator after seeing that. Mine was 17 years old at the time and overall was not looking at its best, the bearings were bad and there was a crack in the outer housing, too. So I figured I'd be better with a brand new one.
Anyway, to be able to replace the slip rings you kind of need to take the alternator apart. And if you do that you'd want to put new bearings in as you got to them and overall the cost of rebuilding an alternator is not much cheaper than buying a new one.