Would prints be better quality on my home printer (HP Officejet Pro) when the image is TIFF / cmyk, as opposed to, say, TIFF / RGB, or PGN / RGB?
Ok, please don't take offence, I did laugh a bit with this posting.
Are you looking for the community for HP Printer products?
Not like I am an expert or even familiar enough to answer home printer questions. However, CMYK is mostly for CMYK printers. most you will not find on the home printer market.
What they do is print each color channel separately on top of each other. C = Cyan, M = Magenta, Y = Yellow, K = Black (Key).
RGB does this also, but only in 3 color chanels. You can still get just almost as high quality as CMYK, however you can save on cost at a print house by only haveing 3 inks to pay for.
After each color channel is printed, you will have a high detailed print. This is what print houses do for flyers, business cards, magazines, posters, etc.
So, to try to answer your question, it shouldn’t matter for your home printer. What matters is resolution of image and what the printer can print up to in DPI. (DPI = Dots Per Inch)
Not sure if giving an answer (even if correct) to a misplaced post is the best idea, if you don't to want to make other lost users think this is the right place to be asking about printers.