Would it be fair to sum it up in this way:while the effects might not be easily noticeable, if you have the capability, print 16 bit?
The potential problem with this is that you might print for the next 6 months before realizing: "wait a minute, everything seems a little off". I've been to enough people's studios that have experienced this - and when we unchecked this one checkbox and saw the color they were supposed to see all along, they were furious. Furious that the solution was so simple, that it took them so long to figure it out and furious that that checkbox was the problem all along.
If people call saying "My color is a little off when I print from Lightroom" the answer is always to uncheck the 16 bit printing checkbox. Seems like this problem is mostly with some Canon printers, but I haven't kept tight notes.
So I tell the masses to be careful and double check their print quality if they use it, and to leave it unchecked if they want to be sure they don't have problems. People usually fall into two camps - one group is detail oriented and wants to be thorough and use this checkbox, the other group is oriented towards the productivity of their image making and wants to minimize failure and doesn't use the checkbox.
I'm a print quality geek but even I think, realistically, you're not missing much by unchecking it but you are ensuring a reliable printing workflow.