I just HAD to check.

My memory being what it is and Alice being no longer here, to ask when I did it, I thought I saw what was a possible deterioration in brightness.
I had to check. I bought a pair of "D" cells and with uncharacteristic skill remembered to do a "before" shot.
It appears I was right; same camera, same settings, same time of day, give or take time taken to change batteries.
Way back here  I changed the bulb without changing the batteries.
Today I changed the batteries.
I think I can safely say there is a visible improvement. Not too shabby though, far a pair of batteries of undetermined age?