Can Alphonse sleep in FMA/FMA:B?
To simply answer your question. No he cannot sleep. I found the below referenced in the fma wikia here.


  Additionally, his armor body has several combat advantages including - strengthened offense and defense, imperviability to bullets, inexhaustible stamina, invulnerability against extreme temperatures and an exemption from needing to breathe, eat or sleep. 


Although, it only states that there is no need for him to sleep. I am 100% sure that in the anime, Alphonse explains Elric about the horror of not able to sleep and the pain he suffers in solitude. It is a very sad situation that almost makes you want to die. 

EDIT:

Found the below content here


  During the night, after Edward's emergency surgery was completed successfully, Alphonse discovered the true tragedy of his new body. Incapable of physical sensation and sleep, he began to feel detached from others and lamented the long solitude of restless night.


This clearly states his disability to sleep.