Earplugs don't block out all sound. Not even close. They do take the hard edge off of sounds, especially like doors closing or the snap of a dog bark.
I started wearing earplugs when I had to sleep on a ship next to a couple dozen other dudes within 6' of me. Still wanted to torture and murder the ones that snored. Still wanted to break the fingers of the ones that set their alarms 1.5hrs before they had any intention of getting out of their rack. I kept wearing them when I worked nights. Now that's just part of how I sleep.
But as far as waking up to the alarm clock, the most important thing, earplugs or not, is to wake up when it goes off and not use the snooze feature. If you've spent your whole life hitting snooze, first, decide when you need to wake up and set the alarm for that time and then get up at that time, but if you don't then you are training yourself to not fully come out of sleep when the alarm goes off.
But honestly, 90% of the time I wake up and look at my clock 3-4min before the alarm goes off and get up. If I actually sleep until it goes off hearing it, even through earplugs, makes me wake all the way up.