Under normal circumstances the rim flanges barely move with the added load of tire pressure pulling them apart. However wear thins and weakens the flange and eventually it'll weaken enough to flex outward.

Fortunately wear isn't perfectly even, so some areas will begin to sag before others causing a pronounced brake pulsing. So no pulsing is the best indicator that the rim is OK. However you can also get pulsing from other causes, so pulsing alone doesn't mean the beginning of the end. If you have pulsing, combine it with other clues such as a concave brake track, and/or clean the rims and shoes to eliminate other causes.

If a rim is doubtful, I use a "safety method" by over-inflating tires by 15-20% to stress the rim, then drop back to riding pressure. That provides a degree of assurance that I won't see flange failure while riding.

BTW- referencing Jeff Wills' test. the rear rim on my commuter is concave by about 1.5mm or so and shows no hint of pulsing or measurable spread under tire load, even at 20% above where I ride it. I was hoping to take it to the point of failure, but unfortunately a nice lady T-boned me last summer bending both wheels sideways beyond salvage. (I was OK, suffering only a bruised thigh and ego).