Yes, it will become easier! But..
The more you practice, the better you will get, the easier playing will become.
There's a few caveats, though.
.. It takes time
Will it be a lot of time? The answer is: not a lot, exactly the time it takes you to learn .
But is too much? Will it be a waste? That's subjective, but I would say it won't be =)
It does indeed take time to play a song solidly. Some of this time has to do with knowing the piece by heart, some with other skills, dexterity, time keeping, musicality etc.. That you might actually learn later on as you progress.
As you go over and over something you'll notice that some stuff ceases being difficult and you can play it while thinking about lunch.
Also, you're playing one hour a day, that's awesome, but it is not that much, so expect progress.
Musician in the early stages practice 8 hours a day, every day.
Try this : take a weekend to play as much as you physically can. This will result in faster improvement and reinforce the idea that it's a matter of quantity of time devoted to it.
.. The difficulty has to be constant
As you progress you'll tackle harder and harder pieces. In turn, it might seems that you are not progressing much at all.
Try going back to older and easier pieces or just learn a new, but purposefully easier piece. Then you can assess the magnitude of your improvements and motivate yourself. You'll be amazed, I promise.
.. You have to practice efficiently
You also have to practice smart. If you're playing the one thing you like and know how to do, your progress will slow down. Either strive for improvement in your practice time or ask find a teacher to push you.
.. Manage your expectations
One of the biggest motivational sink is expecting the time to obtain the desired level to be X and then be bugged down when it takes longer.
The first few times it will look daunting.
Use this first learning experience to form realistic expectations of the time you need to learn something and expect it will take a little longer during practice time.
Look earnestly at your improvements without downplaying them. This is also the result of biased expectations.
Realize that no one knows how long it will take to you to learn something, especially you don't. You're best estimate is the time it actually took once you're done.
While practice does require you to plan and stick to the plan sometimes, look for a balance of exploration of new fun concepts and silly things as well. You have an instrument in front of you, touch it, play with it, do crazy impromptu experiments, do not care if it doesn't sound as it should.
Play songs you love.
Look for details and perfect execution in dull exercises to make them worthwhile and fun.