Absolutely. Either the battery is bad, or there is something wrong causing overcharging / overvoltage
First, chart the battery and have it load tested, or better yet, substitute a know good battery out of another car.
Measure the charging / running voltage at an RPM to simulate "medium cruise" with a multimeter. IF the voltage is above 14.5 at the most, you have a problem.
Some causes:
(You didn't say what year, I assume your 71? In any case later than 69?)
Green wire to regulator could be shorted to ground causing "full field"
Brush hooked to green regulator wire could be shorted to ground, or alternator ROTOR could be shorted
To find out, with system running, unhook the REGULATOR connector. If charging stops, that much is OK
Could be bad regulator
Could be regulator is not GROUNDED, or is not receiving FULL 12V
To test for these two,
1 Hook your multimeter to the blue alternator field wire, and the other probe to battery POSITIVE such as the starter relay stud. Turn the key to "run" with engine OFF. You are hoping for a very low reading, not over .2--.3V (three tenths of one volt) If more you have a voltage drop in the harness. The amount of voltage you read is ADDED to the regulator setpoint, IE if this test reads 1 volt, and the regulator correctly tries to charge at 14, you would be INcorrectly charging at 14 + 1 or 15V
2 Start the car, engine to simulate "medium cruise." Stab one probe onto the battery NEG post, and the other probe onto the regulator mounting flange. As in test 1 you are hoping for a very very low reading, zero would be perfect. Anything above .2V (two tenths of 1 volt) means you have a grounding problem.
If these tests check out OK, replace the regulator. PLEASE spend the money on a good quality one. NAPA Echlin And Standard Motor Products used to be.