9 Avarice Seals
3 Avarice Quints
4 Greed Mastery
2 Wealth Mastery
Avarice Blade
Philosophers Stone
Kage's Lucky Pick
Heart of Gold

Start with 515 gold, get 40.25 gold per 10 seconds. (on SF)

If it's a 30 minute game, by standing in spawn fountain, 7760 gold will have been earned. (with some discrepancies because of the fact that you have to buy the gold items first.)

Would a gold build ever be viable?

Or just for fun to watch cash roll in?

Hi.

If you're in games where nobody can win even 50 minutes into the match, there are many more things you can learn instead of aiming for passive gold generation. If you're in matches that last 30 minutes, getting other items would suit you better. If you're in matches that last 20 minutes, they don't recoup enough value.

The main point here is that anyone with different runes/masteries will have an edge over you for the entire game until you can purchase equalizing items with all the extra gold you've gained. The severity and duration of that disadvantage is too great to justify going full gold generation.

No.

This probably suite for support champions as they hardly have any source of income and they don't need damage and defence as much as other champions. As for any other champions, there are more better choice of runes and masteries to give them more advantage.

Like the old saying, "A good start is half way to success". Other runes and masteires have better chance for you to ensure to get that "Good Start"