Probs a noob question, but my mate and i tested it by dueling and it didnt but i noticed when i didnt pop barrier in raid my heals dropped massively. I generally dont like looking at logs, but one of our healers has taken to quoting them a lot. So do these spells show up as heals/absorbs (and yes i know to merge heals and absorbs) or do they count as damage reduction and hence not show up in absorbs/heals.
Damage reduction (percentages, like Shield Wall, Power Word: Barrier, Barkskin) do NOT show up on recount. You just take less damage, so the person who has the buff will have less "Damage Taken" on Recount. Damage reduction abilities (Power Word: Shield, Blood Shield, Savage Defense, Guarded by the Light) DO show up on recount as Healing Taken / Absorbs.
I would guess that, your heals are dropping when you don't use barrier because you have the glyph which increases healing by 10% under the barrier. Or mentally your preparing to use barrier and are ready for some kind of aoe healing slightly quicker then if you were reacting to the raid damage taken. Besides those I am not sure how using or not using barrier would change your healing numbers.