No, you can't buy everything with Gallantry in one month. The link I provided shows you how many you need to cap a cape, and you can compare that to the list of how many you can buy in a month.
Capes are fully upgraded with:
20 Thread
20 Dust
10 Sap
10 Dyes
5 Resin.
With Gallantry each month you are limited to buying
20 Thread
20 Dust
10 Sap
5 Dyes
5 Resin
So you'll be short 5 Dyes if you're only using Gallantry. Though why you're restricting yourself to only using Gallantry is anyone's guess
https://www.bg-wiki.com/ffxi/Category:Ambuscade_Rewards
https://www.bg-wiki.com/ffxi/Category:JSE_Capes