IF the alternator is actually not on, then YES it will. If the alternator IS on, then you will be fine.
You would probably know really fast if the alternator actually isn't on, I'm not sure how long the battery would last but an alternator died in one of my cars once and it didn't last more than 10 min before the car was dead. That could be because the battery might have been already low??
Either way, the voltage with the car off should be 12ish volts, from your battery.
Turn the car on, if the alternator is working it should read aroun 14ish volts dependino on the specific alternator.
If you still get 12, then the alternator either isn't on, or is just slightly on, but all of it's power is consumed.
If your car uses (just a wild guess) 30 amps at idle, your alternator might produce 25 amps at YOUR ENGINE'S idle. You would then have a negative 5 amp draw, IE your battery is dying.
You can probably talk with the company that built your alternator, ask them how much power it puts out at idle. Tell them what your car idles at, I'm pretty sure in park, most cars are around 1200 ish RPM and in drive 900ish RPM.
Hope this helps,
Good luck,
Craig G