Yes, but... only if they start a syllable.
Die Stadt - the city (with sht) (also: die Großstadt - the major city with sht)
Du bist - You are (wit st)
Das Spiel - the game (with shp) (also: das Beispiel - the example with shp)
Die Wespe - the wasp (with sp)
By the way, in Northern dialects they never pronounce the sh - in sp and st. In Southwestern dialects the always do.