charge batteries while drawing from them?

Can I just connect an off-the-shelf 12v battery charger to each battery, and leave them charging while my motor runs?

Yes, that will work fine.
just make sure both 12v chargers are isolated, or you will create a short on the mains.

to test, measure the resistance between the input and output leads.

Matt

How do you plan on charging batteries while driving? I used a 12 volt Optima Blue top going into an Inverter making 60.0 volts and it didn't charge main pack but going down the road it showed 20 to 25 amperes going into battery pack / motor controller assembly. It sort of increased my range but not by much. Almost as soon as I stopped ammeter went to zero. If it weren't for a generator being so noisy and heavy I'd do a gen set and charging that way but then again generators stink. Now I did that on my VX-1 and still didn't increase range much there either. Range went up but an extra Gel Cell and Inverter was probably too much extra weight. That pack is 125 volt pack and regular household type inverters going into a Full Wave Rectifier can charge the NiMH pack at the same time driving but wires melt on inverter from 12 volt battery. And also bars keep going up to 17 bars. Range went up a tad bit but need to figure better battery pack for inverter. So after 25 miles I swapped out Blue top for a good one and on way home swap out again. Three two hour charges one on each blue top and 2 hours on VX-1. An inverter can get up to 140 volts and fully charged VX-1 pack is close to that.

I'm planning a project in which I have two 12v lead acid batteries wired in series to give me 24v, to power a motor.

I may want/need to charge these while they are in use.