Absolutely not. Or more accurately, not necessarily.
300dpi is a convention for images destined to be press-printed onto paper, for optimum quality. However, 300dpi on its own is meaningless – you also need to define the final printed image size. So, the very same ‘high resolution’ 300dpi image printed at 5″x7″ magically becomes a low resolution image when printed at 20″x16″.
Our 35mm film recorders output at 4096 x 2732px. The image size is 36 x 24mm. So we output at 2890dpi (or more accurately, 2890ppi – ppi = pixels per inch). If we said images must be supplied at 2890ppi many customers would faint at the concept.
DPI is a relative value, pixels are an absolute value. So, for our purposes, ‘quality’ of image is defined by the number of pixels the image is made up from. This isn’t an alien concept – we all know that a high end digital camera that shoots 36mp (mega pixel or million pixels) images is ‘better’ than a snapshot camera that shoots 5mp.
As far as slide production goes forget dpi and ppi, it has no meaningful application. The more pixels, the sharper the slide.
And for those that fret about a dpi setting in Photoshop, you can either put any value in or none, it makes no difference (just make sure you have the resample box unchecked when changing ppi values, so that you don’t accidentally change absolute pixel values).