You will probably wish you had replaced that alternator....
What's a "TBS" besides a TV station that's supposed to be "very funny"??
Get a voltmeter and measure the alternator output while you're running. Should have between 13.8 and 14.2 or so.
FWIW, when my alternator failed last summer, the BATT light never came on (and the bulb is good).
Steve