Start a list and see where it overlaps with this list. It may take a bit, but you should be able to find it out as soon as you hit one of the more rare chests, provided Supercell hasn't changed the order.
As you can see here, the gold contens of a chest very much depends on the arena you currently participate in. You say it is Arena 3 (Barbarian Bowl), so that's what I am assuming throughout the reset of the answer. Higher arena means more gold, so faster gold-getting!
A silver chest will give you (averaged) 38 gold, and a gold chest 127 gold. I disregard the giant and magic chest, see that as a bonus if it pops up :). There are 180 silver and 54 gold chests throughout the whole cycle (source), so roughly 3 silver chests per 1 golden chest. If you open them in order (that is, SSSG), you'll be netted (38*3 + 127) = 241 gold in 17 hours (3*3 + 8).
However, there are also free chests and the crown chests, that add to this amount. You'll get roughly 4 free chests in this time period, and 2/3 of a crown chest. I'm not sure how much this is, feel free to comment this if you are on arena 3 and open a free/crown chest, I'll add it in. This depends on your playstyle: if you play only a few games per day, not enough to win the crown chests, it takes longer. If you play just once a day, you can only open 2 free chests, instead of the theoretical maximum of 6.
Furthermore, you can donate cards in your clan and get money (and experience) in return. How much you donate is completely up to you. As told here, it is a maximum of 4200 gold per week. You'll get 5 gold for a common donations and a staggering 50 gold for a rare donation.
In conclusion, it differs quite much per player. If I can get the gold per crown/free chest, I will calculate the approximated time when you play at maximum efficiency.
Best Answer
Yes, it does. After a not-very-recent update, Elixir Collectors are affected by all the speed-modifying effects. These include Rage, Freeze, Zap, Ice Spirit's freeze effect, Ice Wizard and Ice Golem.