Wasn't many years ago they all did!!
The last sunpack I owned had a DRY CELL ONLY sticker in the batt
compartment.
That was only a couple of years ago.
Like I said you need to check the instructions. But why should I care
if your flash goes pop because you stuck in rechargeable batts when
the flash does not have a regulated supply to control the massive
current dump than can happen with any rechargeable batts that goes
faulty. Working in a shop for many many years I have seen it happen.
Your concept is contrary to electronic engineering principles.
Massive current dumps are not caused by rechargeable batteries (good
or faulty); it's the load that controls that.
Would you believe that some flash units actually depend on the
internal resistance of the batteries to limit the current. There were
only three components in the main charging circuit, the battery, the
primary of the transformer, and a switching transistor. Too low a
series resistance on the battery, and you blew either the transistor
or the transformer primary windings.
Additional current limiting components either added pennies of cost
or increased recycling times.
33 years ago, my first SLR was a Vivitar 220 (hey, I was 13, what did
I know?)
It had a Vivitar flash ($19.95, brand new) that took 9 volt radio
batteries, and required the series resistance of an alkaline or zinc
battery to limit the current. The first time I used a 9V Nicad (even
at 13, things like that were "free": I had a local RadioShack manager
who paid me in small parts for doing repairs) there was smoke. I
replaced the transistor, added a small series resistor, and life was
good.
But I haven't seen anything else like that in 3 decades...