Do enchantments or potion effects that 'Fortify <Magic School>' also affect charge cost of using staves?

Question

I'm asking based on info from the UESP wiki's "Staves" article (emphasis mine):

Anyone can use a staff, regardless of magic skill, and using a staff does not use any of the caster's own Magicka; instead, it depletes the staff's charge. However, the higher the user's skill level in the relevant magic school, the lower the charge cost to use the staff. Using staves does not increase your skills, nor do staves benefit from higher skill levels, with the exception of lowering the cost per charge.

And from a loading screen message:

The charge level of a staff is based on the corresponding skill of the mage wielding it. For example, a wizard with a high Destruction skill would get a lot of uses from a Staff of Fireball.

I'm wondering if 'Fortify <magic school>' alchemy effects or enchantments (make spells cost less to cast), also could affect the charge cost of using a staff of the same magic school.

For example, if I'm wearing a robe or armor like the Robes of Extreme Destruction or Vampire Armor of Extreme Destruction (Fortify Destruction, 22 pts; Enchantment description: Destruction spells cost 22% less to cast) – will those apparel lessen the charge cost of using Destruction staves like the Staff of Fireballs or Staff of Ice Storms?

Answer 1

Yes. Most easily seen by enchanting yourself 4x -25% destruction pieces (Helmet/Necklace/Armor/Ring).

If you want to confirm quickly, you can use the console command
playerenchantobject <object> <effect 1> <effect 2>
This creates a given item with the given enchantments withe magnitude of your current enchanting skill. So for example - to get a necklace with fortify destruction:

playerenchantobject 877f1 7a0f6

Combine with modav enchanting <x> (or setav) to make your enchanting 100 to get a -100% cost item with that command.

Answer 2

From my hours on Skyrim, if you wear any armor or robes that decrease the cost of spells, then it will NOT decrease the spell for staffs. Although I was only a mage to finish the College of Winterhold questline, I still paid attention.