Yes, it can be done, but there are a few challenges. You have an aluminum frame which means the dropout width cannot be altered. It is almost certainly 135mm, but confirm this before moving ahead.
Since you have vertical dropouts, you will also most likely need a tensioner of some sort. Your derailleur could serve in this role. There is an outside chance that the chain will run within acceptable tension without a tensioner. I have two bikes with IGHs in vertical dropouts without tensioners, and have done other builds where it worked out this way, so it can happen.
Many Sturmey Archer hubs are flexible when it comes to over locknut dimension if the axle is long enough, you can stack spacers and nuts to space it out as required, but the best and easiest way to ensure correct chainline is to start with a hub already spaced correctly. In your case, I would recommend this model.
https://www.sturmey-archer.com/en/products/detail/s-rk3
It is the disc brake version, but it can be used in a rim brake application, and it comes only in 135mm width, so it should fit right out of the box, and dialing in the chainline should be a simple matter of flipping the dished cog to the most suitable line.