Converting comments to an answer.
We've had problems regarding software upgrades via Prime on new equipment, like the 3650, 3850, 9000 Series from Cisco. Prime is not setting the bootvar correctly and often, this results in the switch not being able to boot or not being upgraded i.e. rebooting on the old software. We've created a TAC case with Cisco, but it's low priority.
We haven't had problems with the 2960S/X series luckily. We have about 2000 of these and they've not produced any problems when using Prime to upgrade them. Last time 1% didn't work, but that was hardware related. The only flaw to note is when Prime tries to upgrade this type of switch and the flash is full. This will generate an error while deploying fortunately.
I'm pretty confident, that you can upgrade your 2960S/X series without any problems.