Is my bike capable of swapping for longer cranks?
Yes, your bike is capable of using longer cranks.
Longer cranks will likely cause more toe overlap, which is generally expected and widely tolerated on small-framed 700c bikes. Here is Sheldon Brown's opinion of toe overlap, from his online glossary:

On many bicycles, especially those with smaller frames and full-sized wheels, it is possible for the front fender or tire to bump into the rider's toe or to the toe clip. Some people worry a lot about this, but it is rarely a significant problem in practice.
The only time it can happen is when the handlebars are turned quite far to the side, as only happens at very low speeds.
Many, many people ride bicycles with fairly severe overlap with no practical problems, sometimes having to make a slight adjustment to their pedaling habits at very slow speeds.
On smaller-size bikes with full-sized wheels, it is usually impossible to eliminate overlap without causing adverse fit/handling issues.