You can. it would just take a really, really long time. A Pokemon earns one experience point in the daycare for every step you take. A Pokemon can have anywhere between 600,000 and 1,250,000 experience at level 100. That means, from level 1, you'll need to walk anywhere between 600,000 and 1,250,000 steps to reach level 100 from daycare experience alone.
Is it possible? Yes, but training them to level 100 the old fashion way or winning rare candies at the battle maison would probably be more fun.