It depends on the sect, but yeah for the most part it is. Once they cross that line it's Mennonite. but there are some sects, like the Swartzentroubers, that are very old order and don't even wear shoes. But for the most part they won't. Even the dolls at Amish stores don't have faces. And they may make exemptions for hijabs but there still has to be a photo and they just outright refuse for the most part, except for during rumspringe

not having a picture on your id would defeat the purpose of your id.

making an exemption would create a loophole more nefarious actors could easily exploit. no sane dmv is going to get away with instituting religious purity tests to make sure everyone who says they are amish is actually amish.