total N00B question

is it feasable to power an arduino that's being used as a battery charger from the battery that is being charged?

_Yes but how do You intend to get started when the battory has gone flat?

Yes. If it's a 12V battery you can use a buck converter to take it down to 5V or to 7V and feed that to the power jack/VIN regulator for a cleaner power if say you want more accurate analog reads. 5V off a DC converter will run a 5V Arduino okay.

The DC converter will handle voltage up and down between charging V and battery V.

Buck converters are very efficient, they don't heat up so much as inefficient linear regulators.

Railroader:
_Yes but how do You intend to get started when the battory has gone flat?

Plug in another battery of course, or solar cells with a boost converter if you have time.

I have cheap boost converters with USB charge port on the board.
They take .9V up to 5V in and give 5V out.
You can drain “dead” batteries in series to charge a phone ferinstance.
Or power a project from a solar panel giving < 2V.

GoForSmoke:
Plug in another battery of course, or solar cells with a boost converter if you have time.

I have cheap boost converters with USB charge port on the board.
They take .9V up to 5V in and give 5V out.
You can drain “dead” batteries in series to charge a phone ferinstance.
Or power a project from a solar panel giving < 2V.

You would and can do as well as I but what’s the options for OP?

Try.
Learn.

Trickle charge.

Railroader:
_Yes but how do You intend to get started when the battory has gone flat?

GoForSmoke was right, it's going to be solar power