I don't know about collecting seeds, but you won't have any trouble moving/transplanting it. If, in the future, you should change your mind, you will be out of luck. It's one the rare true blue flowers and is an attractive plant to me and can be spectacular when it's blooming, but I've never been able to get rid of it when it grows where I don't want it and it's quite efficient at spreading around into places where I don't want it, so I'm sure it must spread from seeds. It grows from a rather long fleshy root and apparently even a small piece of that root that is left will regrow into a plant. It breaks off easily when you attempt to pull it, so I find it impossible to remove.
I'm not sure where it came from here. I have a whole pasture that I walk around in and yet I've never seen it growing anywhere except here at the house, so I suspect it got transported in somehow or the other. I do like it well enough that sometimes I just let it grow rampant even when it's among other plants. Here's a photo of my Commelina 'Dayflower' that grows here. It's accurate for the color here which appears more blue than in your photo. I think there may be a more purple version of it.
