it's not unknown for a recon alternator to have had nothing more than a clean up and a blow over of new paint....in fact it's pretty common.....
There's a couple of simple chacks you can make yourself before shelling out to someone else- firstly, ensure that the alternators drive belt ('fan' belt) that goes round the pulley on the end of the alternator is correctly tightened- you should be able just to deflect it at the mid point of its longest run under firm thumb pressure. If it's flapping about loose then it won't drive the alternator fast enough to keep the battery charged.
If you have a multimeter (you can get 'em from maplins for about a fiver..)and you can use it to check the alternator's output- set it to the 0-20v range and put it on the battery, and with the engine not running the battery should read about 12 volt or just above. Start the engine- the reading should now be somewhere between 14 and 15 volts, varying only slightly with revving, if the alternator is charging correctly. If it stays around the 12v mark, then it's a fair bet that the alternator isn't charging, in which case take it back where you got it from!!