"I can see" is usually used when "see" is meant literally -- "I can see a ship on the horizon".
However, it can occasionally be used in situations like the following:
"If we want the world to be a safer place, we need to invest more in the military."
"Yes, I can see that, but for that to work, we also need....."
"Well, now that I know she has four children, I can see why she has so little time."
In such contexts, yes, "I can see" means something very similar to "I can understand". However, you can't do this in all circumstances. In MrP's examples, "I can see" would not be a good choice. It's probably best to avoid "I can see" if what you mean is "I understand", and use it only when you really mean "see".