Yes, old grass is a really good tell. It is really hard to describe this, but older grass just looks weaker and darker in color, maybe a bit patchy with bald spots. Newer grass seems thicker, greener and healthier.
Newer grass can suggest resodding or grade and fill, which is bad. Older looking grass suggests the lawn was less likely to have been tampered with.
Also, as I understand it, soil is the result of earthworms eating grass. The thicker (newer) the grass, the thicker the soil, thus the deeper the coins. Digging modern clad (as opposed to 60s and 70s clad, which is a good tell) at 7 inches in thick grass is not fun, and a tell the site is likely a dud. OTOH, get a patch of old grass or bald spot under a huge old tree, and you can find 1800s coins at an inch or two. Of course, tree roots also help stop the sinkage.
I do not think that there is a hard and fast rule. It is a ton of factors and a ton of experience to asses whether a site will be a dud or a honeyhole. Throw some of the suggestions from this thread, and others, into the pot and let it simmer, and get out there, be observant, and eventually you may get a 6th sense about this stuff. A key is to quickly assess where the site is on the dud -> honeyhole meter, so your time can be spent most efficiently.