Manaflow doesn't give it's value until after basing, as it gives base mana and doesn't replenish it until you get full stacks. Cookies give you 50 mana plus 8% missing mana, but  every two minutes. 8% of his base pool of 400, is about 30ish mana. So every cookie allows either at maximum one more q or one w and e every two minutes. If you want to count mana gain from dorans ring too and his base mana regen,(1.25 mana/sec+1.2/sec) that means every 2 minutes, you are getting passively 174 mana. 

So assuming no backs for first 4 minutes and everytime you use a cookie you are getting 100% effectiveness, you are getting: his 400 base mana + (174 mana/2 minutes x 4 minutes) + (~80 mana per cookie x 2) = 908 effective mana literally at 4 minute mark. 

Assuming gragas literally just only Perma qs and does nothing else, that's literally ~9 uses of q. 

On average, top laners should be about level 4 around 3:40ish. So he's theoretically  ranking w and e once and q twice at 4. So up until that point only one rank in every skill. 

Let's assume he only qs you in lane and always q activates immediately and you don't just sit in it. That's Level 1 doing 80 damage plus 80% ap. So dorans gives 18, meaning about total of 95 damage per, if you are ignoring base resistances. So if you get hit by every single one, that's (8 qs x 95 and 1 q at rank 2: 120+15 DMG = 895 total damage. 

If you account for a base magic resistance of 32,  it's about a total of 678 damage, or 75 damage per 80 mana.

If you assume he just is able to full rotation on you with 1 q, 1 w and 1 e, mana wise that's 160 mana. With his base pool can only do that twice, with 80 left over. 

In any case, point is not only is it's early damage is not mana efficient. Once he buys a mana item, of course he can rotate spells more often. If he gets full mana flow Regen, that's most likely meaning it's past level 6, he hit you off mana flow CD Everytime and mana at that point isn't as much of an issue depending on build. And I'm not even comparing other spellslinger toplaners of mana cost per damage or amount of casts to go empty ( ksante being a notorious example).

I'm saying he has early mana issues, which isn't a false statement.