No, you can perform SHA256 on a file (and U do on every update), but performing a verification on the firmware itself would require SHA256 code in the firmware. (Which there is, in a way - firmware that doesn't pass the validity check doesn't get past the loading stage, which is why many phones get stuck in a "boot loop". And why phones aren't shipped rooted, the way Linux itself [Android is an app that's running in Linux] is.)
Unless you have some cheap no-brand phone, if it gets to the homepage, it's passed "safetynet" and a few other checks that verify that it's real. (That doesn't mean "no viruses", it means that the Android installation is valid. It's like checking the spare to see if you have any flats - there are other tires, but if you don't check them, the spare could be fine, but you could still have a flat somewhere else.)