Can I safely use rectified 120VAC to keep a 120V lead acid battery charged?
TL;DR Any quick/cheap method will probably damage and shorten the life of the batteries, especially if connected in a big series string.

A battery charger is more than just shoving charge into a battery. It also has to do no damage, to you, and to the batteries.

To you. It needs to be isolated from the mains. This means a transformer.

To the batteries. That means you have to respect the maximum charge rate and voltage at all times, which means a peak measurement. Unfortunately when you measure raw rectified AC, most meters will make an average measurement, and so underestimate the effect of the current on the battery. If you are measuring it with a meter, you should use smooth DC to get correct measurements.

You don't say whether you are using sealed or wet cells. Wet cells have greater tolerance to overcharging, as you can replace the lost water by topping up, although gassing 10 batteries at the same time will generate a lot of explosive gas, make sure you have adequate ventilation. Sealed cells must not be allowed excessive current during float, as this will result in a permanent loss of water to the battery. Usually this is done by limiting the voltage to around 2.3v per cell (with ideally a temperature coefficient applied), but can also be done by checking the long term float current (expect current around C/1000, C/100 is too high). 

Normally, for battery balance, I'd say you don't have to worry about for lead and nickel chemistries, and they balance themselves on over-charge. However, this is only at float currents. With 10 batteries in series, if you're only monitoring the voltage from end to end, one cell could suffer severe water loss while the other cells are still accepting charge. Unfortunately, with the target float current in the C/1000 region, that makes for a very long float charge and balance if done by float overcharge alone. 

If you want to recharge your batteries between experiments at a reasonable rate, then you need at least some form of per-battery voltage monitoring, if not active balancing, if you do it with them connected in series.