It definitely will save ppi tag when file is saved as Tiff,Psd,JPG.
(it won't save the tag if Save For Web is used).
Btw, be sure you have Resample OFF when changing from 72 to 300 and
you'll be using only original pixels.
If you are saving files at 300ppi, then when you reopen them, it's
showing 72ppi, then something has gone awry.
Try deleting prefs in that case.
Mac
Untagged images do indeed open at 72ppi, as they do in most programs by
default. Some proggies, like PaintShopPro, let you set a default ppi for
opening untagged files.
Mac
That will not override any ppi tag already embedded in existing image
header.
Or EXIF ppi from digicam file.
Or absense of either of those tags in existing image. If no tags at all,
will still use 72.
Mac