Ok, done.

code/modules/modular_computers/computers/item/computer.dm

@@ -26,6 +26,7 @@
 	var/icon_state_unpowered = null							// Icon state when the computer is turned off.
 	var/icon_state_powered = null							// Icon state when the computer is turned on.
 	var/icon_state_menu = "menu"							// Icon state overlay when the computer is turned on, but no program is loaded that would override the screen.
+	var/display_overlays = TRUE								// If FALSE, don't draw overlays on this device at all
 	var/max_hardware_size = 0								// Maximal hardware w_class. Tablets/PDAs have 1, laptops 2, consoles 4.
 	var/steel_sheet_cost = 5								// Amount of steel sheets refunded when disassembling an empty frame of this computer.
 
@@ -208,20 +209,26 @@
 	else if(obj_integrity < max_integrity)
 		. += "<span class='warning'>It is damaged.</span>"
 
-/obj/item/modular_computer/update_icon()
-	cut_overlays()
+/obj/item/modular_computer/update_icon_state()
 	if(!enabled)
 		icon_state = icon_state_unpowered
 	else
 		icon_state = icon_state_powered
+
+
+/obj/item/modular_computer/update_overlays()
+	. = ..()
+	if(!display_overlays)
+		return
+	if(enabled)
 		if(active_program)
-			add_overlay(active_program.program_icon_state ? active_program.program_icon_state : icon_state_menu)
+			. += active_program.program_icon_state ? active_program.program_icon_state : icon_state_menu
 		else
-			add_overlay(icon_state_menu)
+			. += icon_state_menu
 
 	if(obj_integrity <= integrity_failure * max_integrity)
-		add_overlay("bsod")
-		add_overlay("broken")
+		. += "bsod"
+		. += "broken"
 
 
 // On-click handling. Turns on the computer if it's off and opens the GUI.