Question: I had one on my Beretta that only charged at about 50% of it’s capacity for about a week before it completely died.. If I didn’t use alot of accs’ (AC, etc) It would sufficiently charge the battery to start the car up..
However, it did eventually die..
As for the rest of your question, yes, the car will start (And run) as long as the battery maintains a charge, which, without an alternator, won’t be terribly long.

Answer: I had a lemon 1987 IROC (Camaro Z28) that went through 3 alternators. The first time was a real circus. On a drive to a friends house about 30 miles away, I noticed the voltmeter had dropped to a bit less than normal battery voltage and did not vary with RPM. I knew immediately that the alt was dead. Nothing to do but keep going and hope I made to their house. Made it OK and got out their battery charger in hopes of charging the thing overnight to have enough juice to get home the next day. But they had only a 1 amp motorcycle battery charger. :( Charged all night. Started up and headed home in the AM and got within 2 miles of my house when she flamed out. On a narrow road with no shoulder. In rush hour. All I could do was to push it off to the side as best I could. Got a ride home and pulled the battery out of my other car and a neighbor took me back to the ROC. Put it in and drove home.
The rest of the story is ugly, too. The alt failed when the car was just out of warranty and it was apparently a new alt design, so there weren’t any rebuilts on the market. Had to cough up something like $250 for a new one. That was a lot in 1988 or 89. And I had to get someone to drive me halfway around the beltway (DC) to get it. Quite a shock as I had replaced the alt on my old firebird a year or 2 before for $25. What a nightmare.
Damn thing failed 2 more times before I finally rid myself of the lemon ROC.

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