well... it's inefficient to run the light off of half of the AC waveform, and it's pretty inexpensive to use a full wave bridge rectifier, so I'd be surprised if a commercially produced light wasn't using a full wave bridge rectifier.

Regardless... this wouldn't be an indication of whether it is advisable to run the light from a 5V battery. Like any diode, there is a threshold voltage (called "forward voltage") for any diode.... if you apply a voltage below the forward voltage, almost no current will flow. If you apply a voltage greater than the forward voltage, lots of current will flow. A lot of white LEDs that you see in bike lights are rated for 1 amp or so, while batteries can supply a lot more than this. I think I regularly see over 5A out of AA nimh cells when shorted.

As such, the concern isnt' so much whether the power source is AC or DC, as the bridge rectifier will accept either. The bigger issue is whether anything is limiting the current that will flow through the LED(s). Some dynamo lights rely on the dynamo's internal impedance to limit the current, and would likely be killed if connected to a battery that could source a couple of amperes.

Other dynamo lights use a switching power supply to provide a better match of the dynamo to a single LED.
For instance, if you just rectify the power from a dynamo and feed it through a single white LED, you'll get a half amp of current. The LED's forward voltage is about 3V, so you'll get 1.5W of power into the LED. Not bad, but that's half of what you'd get with a standard 12 ohm load for the dynamo.
If you use a switching power supply, you can convert the dynamo power from 6V@0.5A into 3V@1A, letting you put 3W into the LED. Much better! A side effect of this is that the switching power supply (i.e. buck converter) is intrinsically current limiting, and should not mind being powered from a battery.

I haven't peeked inside many modern dynamo lights. A couple of years ago, I did fix a fellow's Supernova Triple headlight, and it did not use a switching power supply, and in fact was killed when connected to an e-bike's battery. Too much current flowed through the light, destroying almost everything inside.
The other light that I've looked at is a dead B&M Lumotec Eyc. It does appear to use a switching power supply, based on the use of a 22uH inductor...

(the square item with "220" on it)


The square integrated circuit above it is probably a microcontroller.. i.e. the brains of the light. There is a chance that it is looking for AC at the input, so it might just shut off the main light and only power the standlight if there is no AC present. For that reason, the light wouldn't be damaged by DC power, but would not operate from DC power.

All of this just goes back to my original comment.. (IIRC)... without detailed knowledge of a particular light's design, it's very difficult to predict whether or not it can operate from DC power.

Steve in Peoria