No, it won’t as the system date and the expiry dates won’t have changed.

Using system restore can come with unexpected consequences also, it isn’t a backup tool, it doesn’t cover everything, so you can end up worse off than you were previously. I gave up on system restore many, many years ago in favour of using hard drive imaging software. This makes an exact image of your hard drive/partition, so when you restore an image of your drive you get exactly that, not only some files, etc. being covered by system restore.