Chris,
You didn't say what type of airplane or what kind of battery you are using. If a lead acid battery, you were probably fine allowing the aircraft system to charge the battery following engine start, but you do need to pay close attention the ammeter. If you have volts and amps monitoring capability, you need to check both. A high rate of charge and a high voltage means you need to shut down and remove the battery for service, and also probably remove the charging device (generator or alternator) for service.
After a low battery condition, you're going to see a high current flow...your electrical source is supplying more current to charge the battery...or more accurately, your battery is drawing a high electrical flow to recharge itself. This is normal.
Most maintenance publications will specify what the minimum voltage is before the battery must be removed for service. Most publications will also tell you not to charge a battery in the airplane. In the case of a lead acid battery, the danger is far less than a NICAD battery, but there's still a danger. Explosive gasses are produced during the charging process, heat is a byproduct of charging, and the gasses released from the battery during charging are corrosive; these enter into surrounding faying surfaces and in the presence of moisture will cause corrosion.
A NiCad battery is different. If the battery is discharged, you should have it serviced by a proper unit outside the aircraft. This is not a simple process, and the battery will probably need to be deep cycled, and may need direct maintenance. Recharging the battery from a discharged state may result in a thermal runaway, in which the battery temperature continues to increase until it can literally melt through the battery tray and fall out the bottom of the aircraft (a NiCad battery can do that just sitting on the ramp, incidentally). This isn't a common occurence, but it's a real consideration when charging a NiCad battery. Don't charge them in the airplane, and always refer to the maintenance publications for the aircraft and battery (often completely different sets of publications) for charging and service instruction.
Many aircraft manufacturers publish guidelines that dictate when you can use ground power vs. when you must remove the battery for servicing. Usually these specify voltage values. Never make assumptions about your system based on anything but what the manufacturer has provided; turn to that for direction.
The fact that your system was showing a high rate of charge following your ground start is quite normal. If your battery is completely discharged, you're better off removing it from the aircraft and charging it slowly for 24 hours before reinstalling it. The battery should also be checked per the maintenance manual prior to reinstallation, and should be load checked.
If the battery was just down a little after several start attempts, you may be able to leave it attached to ground power; leave it attached for at least fifteen minutes before attempting to start the aircraft or use the battery. Monitor the battery during the charging cycle. Batteries do bubble or boil during charging sometimes, especially with a high rate of charge. Check the case for warmth; discontinue the charging cycle if it's hot, and stay clear of it. During charging, generally one should loosen the battery caps for more adequate venting.
Keep a fire extinguisher handy and be prepared to remove the charging source from the battery. Wear eye protection any time you are doing anything with that battery. It only takes one very small droplet of acid, or even residue or grease that's contaminated, to ruin your vision for the rest your life.
Whenever you have any kind of fault, be it electrical, mechanical, pneumatic, hydraulic, fuel related, powerplant, whatever, always determine the cause of the fault before attempting to correct the fault. In this case, find out why the battery was low in the first place, and correct that. If it was a hard start or a series of start attempts, then find out why the engine didn't start before you wear it down again. Starting causes a high current flow, and I've seen the terminals melted right off a battery during the start process after the pilot pushed the starter limits and duty cycle. Don't do that. Find the cause, fix it, recharge, then do a normal start.