Just for information, in my Gossen Multisix, which is designed for alkaline 9V batteries, I use NiMH Tensai 8.4 V. I don't remember performing tests but, if the battery is in there, it means I performed some tests and the battery gave the same result.
My general rule of thumb with electronics is: if a device designed for alkaline batteries does not complain with fully charged accumulators, then it should work well.
If the device complains of "low-battery" state with fully charged batteries, then it could work well or it couldn't, one has to make some tests.
I ignore the instructions to feed the device "alkaline" batteries because, in user-manual parlance, that means that they advice against zinc-carbon batteries.
Only if the instruction booklet explicitly says not to use rechargeable batteries, then I do comply or don't buy the contraption.