Certainly the single dot display (only supported on HP 35, 45, 55, 65 and 67) causes the minimum power drain. On other models, where the decimal point is "merged" with a digit position, a "1." display gives the minimum drain.
The first case (decimal dot only) turns on just one LED "segment". Further, in some models, the current applied to such segment is somehow less than the current for the other segments. Because of multiplexing, the dot is excited only 1/15 of the time, but the refresh rate is enough to fool our eyes into seeing it as permanent.
On Woodstocks and Spices, the "1." excites three segments during 1/12 of the time, so the current is not as low as in the Classics, but it is the minimum possible. I assume that individual segment currents are similar between models, but this is an unproven assumption.
You are right to remark that pressing the decimal dot key on a Classic, or the "1" key on the other LED models, is enough to reduce the display power usage to a minimum (at the expense of a stack lift operation), with no need to change the display mode, as my previous posting suggested.
The power budget for LED displays is a significative part of the total power budget for these models, so batteries will last longer when few segments are active. Apart from this, since LED show no wear over time, there is no benefit in keeping them off. Perhaps my usage of "screen saver" was not a good metaphor at all.
All the power considerations are useful for the older models, but on a 34C, due to the Continuous Memory feature, turning the calculator off (even for a short time) is always a most valid option.