Not really. Dragons get unique versions of all of the Shouts that act as spells, so if you can drain a Dragon of all it's Magicka it becomes incapable of Shouting. That's what makes Shock Magic particularly effective against Dragons, it forces them into melee range and for a Mage, well that's fine as long as you aren't anywhere near it. Here's the UESP page description just because it says it better thann I do. 

Dragons have their own unique "dragon" versions of the Fire Breath, Frost Breath, Unrelenting Force, and Drain Vitality^DG shouts, and their Fireball and Ice Storm spells are treated like shouts as well. Dragons rely on their magicka reserves to use these shouts, which means that if a dragon's magicka is drained, it will not be able to use its shouts. The base damage for all the dragons detailed below is 25 (with the exception of the Skeletal Dragon), and their tail swipe attacks will stagger all enemies in a large area. - UESP, Dragons

Thanks for clearing up my laziness guys!

Soooo I have an idea for a new Skyrim build and I need to know what's the quickest to obtain staff from the start of the game?

err, the Staff of Paralysis can be gotten at level 1 from Snapleg Cave. Also I'm pretty sure you can get staves of Firebolt, Turn Undead, Magelight, Fear from Shalidor's Maze, also at level 1. Just... be careful of the Frost Trolls in Labyrinthian. Is that what you're asking?

[blockquote][b][url=/profile/Noodles]Noodles[/url] said:[/b] Shalidor's Maze it is! Thanks everyone![/blockquote]

It's rather sad that staves don't level up along with the player... not sure if there are mods that do that.
Illusion staves would especially benefit for it.

[blockquote][b][url=/profile/Noodles]Noodles[/url] said:[/b]

Soooo I have an idea for a new Skyrim build and I need to know what's the quickest to obtain staff from the start of the game?

[/blockquote]

Little late to responding to this but there is a Staff of Fireballs on the mountain east of the Thalmor Embassy, can be obtained at level one just look out for some Sabercats.  there is also a Staff of Revenants in an unmarked nordic ruin south east of Morthal.

[blockquote][b][url=/profile/Vargr]Vargr White-Tree[/url] said:[/b]

[blockquote][b][url=/profile/Noodles]Noodles[/url] said:[/b]

Soooo I have an idea for a new Skyrim build and I need to know what's the quickest to obtain staff from the start of the game?

[/blockquote]

Little late to responding to this but there is a Staff of Fireballs on the mountain east of the Thalmor Embassy, can be obtained at level one just look out for some Sabercats.  there is also a Staff of Revenants in an unmarked nordic ruin south east of Morthal.

[/blockquote]

yeah, the saber cats are fun. Lots of running. But... if you play a patched game, Helgen gives you a staff of Frostbite in the cage where the mage is.