For most home printers, yes.
However, even if you have to convert to 8bit at a later date, the fact that /if/ you are performing an operation like one that I mentioned, a whole shift in colour ranges, then there is more detail that will be saved/recovered/available by keeping the colour depth high until the very end.
For example, if you were to take a 12bit RAW image, opened into 16bit tiff, and expand the last quarter of shadows to be 75% of the total range (as if you are trying to recover a dark image), if you did the same with a 12bit image immediately converted to a 8bit image.
For the 8 bit image, you probably only have around 128 levels left in the image, unless the software interpolates the levels that it sees, in which case you still have the full range, but, they will probably be averaged.
For the 16bit conversion, you would have around 32 thousand levels still available. Even if the software is interpolating, that is a lot more information. If that is then mapped to an 8bit file, you throw away information still, but, it is less damaged by having to have been averaged out first.