Apart from producing a larger file and being able to produce a larger print, will scanning at a higher resolution give you more detail?

Example
If from a 4x5 negative, I want to create an inkjet print which is 16 x 20 inches then in theory in the scanner software, I could set the scan resolution to 1440 which would give me 16x20 inches if I sent the file to the printer at 360ppi

Question
Would I gain and more detail in the scan if I was to say scan it at a resolution of say 2400 and then down size in Photoshop when ready to print ?