Yes, but you won't gain much support from non-climbing shoes. Climbing shoes are designed to give you the maximum amount of support for your feet while climbing, even the cheapest beginner shoes.

Regular everyday shoes are over-stuffed with rubber to the point where you wont even feel what you are standing on. This will make climbing very difficult later on. For beginners climbing very beginner-friendly routes, though, it may not make a huge difference since they probably wouldn't even notice the performance gains from the shoes, they will be too focused on how uncomfortable they are. But, as you get better and advance up the ladder, you will notice the difference and understand why climbing shoes are the way they are.

Climbing shoes can be comfortable! But, that is in comparison with other climbing shoes, and not with everyday shoes. I believe that climbing shoes will never be as comfortable as everyday shoes.

If you manage to find the right pair of shoes for your feet, though, they can be very comfortable, considering they are still climbing shoes.

For me, the best way to break them in faster and to make them less painful was to just wear them. The more I wore them, the softer they became. One thing that really helps is to heat them up a little bit before putting them on with a small heater or fan, just enough to soften the rubber a little bit, not too much though to not damage the shoes.

Another thing that really helps and that is very simple to do is to just bend, twist, and fold the shoes for a minute or two. This really softens up the rubber and makes it much easier to put on and less painful to wear.