To do this, you need a lot of energy, it is essentially charging a battery. If this was really feasible wouldn't we be using solar panels to separate water into hydrogen on Earth? Do solar panels in space have the potential for far greater energy output due to less atmospheric constraints?
Plus, if you're not near any objects that can block the sun (i.e. Earth/Moon), you get full, intense sunlight 24-hours a day.
And you can use some of that sunlight to just directly heat the water, which makes it easier to split.
Given all that, I'd say that it's very likely you could get enough energy to split water in space.
We do. If you buy commercial hydrogen, it was probably extracted by water by that process (although other processes are possible), using energy from the grid of which some percent is solar.
So what exactly is your point anyway? The needs in space are far different than on Earth. Solar energy is abundant and available 24/7, but stored energy is needed by rocket engines in large amounts and all at once.
Moving the fuel to release such energy to space is almost by definition cheaper than moving the separated storage medium.