Okay, let's calculate. If something is incorrect (I'm writing this from memory), please correct me. Difficulty is 200%. Gogs are built.
According to your tactic, it works out like this:
Day 1: Prefecture (2500 gold).
Day 2: Demons (about 2000 gold).
Day 3: Ifrits (about 3000 gold).
Day 4: Stronghold (2500 gold).
Days 5-7: Castle (5000 gold).
The approximate cost of expenses for a week is 15000. Income (Prefecture plus Octavia, minus 500 gold for one day, since she wasn't there on the first day) is (1350*7 - 500) = 8950 gold.
Then 15000 - 8950 = 6050 gold.
That is, we need to collect six thousand five hundred gold in a week, which is just lying around on the map. This is the minimum.
Then we simply build up in the Castle. And on the first day, we will have the same

1350 and another collected pile of gold (about 3-4 thousand) to buy 5 Ifrits and... some more Gogs.
Of course, six thousand is about 4 treasure chests, plus another pile of gold of 3-4 thousand. This is an average scenario for a map. My calculations are approximate.
In general, if everything adds up, we buy these Ifrits or part of them and Gogs with the remaining money.
This tactic will work, but it's not the fastest development.
By buying the second and third heroes (that's another 5 thousand), we can raid the dungeon, take treasure chests and gold for at least that amount, plus an army, and heroes that will be useful later, plus the hero gains 2-3 levels.
And reading reports from tournaments, they even manage to take the first rations, dwarves, and Naga banks in the first week.
So, your tactic is not yet the limit of speed. ;)