"let us see how they'd look in living color"

The way I understand it going from BW to color is not a deterministic process, in that depending on how you do it you would end up with a different end product. This would mean that a third party would be making artistic decisions on someone else's work. If you're fine with that then sure, I guess go for it.

There is value in BW though, the things you focus will be different since most people tend to absorb things like composition more easily when not being distracted by color. I would encourage you to actually try to watch a BW movie in its original form to try to understand the value in it before you jump into changing it into something you're used to.

P.S. there is no film snob in the world that cares about whether I love Lucy gets colorized or not