The short answer is yes but you wouldnt want to. The charging current meant for the batteries will be shared with whatever you are powering. If however, you use more than what is given to charge the battery it will still discharge even when plugged in. So it will definately lengthen the time to charge it to say the least.

Plus it will increase the voltage imputed into the ez-b right?

If you are still going through the ezb and it is within the range the voltage regulators can handle, that wont matter. It will still get brought down to 5 volts/3.3 volts. I dont recall exact maximum. I think I saw 17v someplace. Someone will correct me soon if that's not right.

I meant the v4 sorry.

Well, right now im in a rut because to power the servos right off the v4 you need 4.5-7.2V. If I run the ez-b of 12v I'll need to either:

1. Regulate the incoming voltage, which depending on the regulator with bring down continuous amperage.

2. Use the 5V regulator attachments that Dj made and will be coming out soon and sacrifice the ability to run the hd servos at full capability.

If you think 1 could you try to find a regulator that has high amperage?

Seems to me that if you have the regulator on it where it powers the board it wouldnt matter as long as the regulator can handle the charging voltage which will be a few volts higher than the battery. (Depending on battery chemistry)

Charger---> Battery---> Voltage reg---> EZB

Ok so I'll be ok with using a regulator for the v4 and still be ok with charging while running so long as the voltage regulator supports the charging voltage.

I plan to charge mine while in use. However the use will be minimal (i.e. EZ-B running but no movement of any servos or motors). It will take longer (depending on what's running) but I need to have ARC constantly monitor the charge status and the battery.

Provided the charging voltage is not beyond the maximum voltage of anything that's drawing power while charging (EZ-B or regulators) you should be fine. And chances are, unless you are charging in some weird, unorthodox and unsafe manner the charge voltage will be below that max voltage.

@Troy, you are correct, 17v is the max for the V3 (just to put your mind at ease).

@Techno You will probably struggle to find a decent regulator with high amperage (usually due to the PCB traces - don't take the actual regulator data for granted, if the copper isn't good enough for the load it'll cause problems). You may be better off using multiple regulators. You could parallel them to increase the current however be aware that this is not always exact and can cause slight differences in potential between the regulators. It's covered in a topic somewhere else here and also This topic on anandtech forum covers it too.

Multiple regulators it is!

Troy gave the most help but rich you helped a fair bit too. I guess I'll give it to Troy