Does the Celtic alphabet contain ascenders and descenders?

There is no Celtic alphabet. All Celtic languages (Irish, Welsh, Manx, etc.) use variations of the Latin alphabet, since they were first written, around the 6th Century CE.

-- True, BUT Celtic lettering is distinctive (as are many other regional forms, such as German Fraktur).

If you look in "Related links" at the linked graphic of the Gaelic alphabet, you'll see that it has both ascenders -- on B, H, and L -- and descenders -- on F, G, P, R (lowercase only), and S (lowercase only).