It seems that there is no support for Arcade expressions in the pop-up configuration of the image service layer. Would be a great addition (so please create an idea here: ArcGIS Ideas and I will certainly give it my vote!)
Working with raster data is a bit different than working with vector data. See this example below in London (temperature is expressed in °C):
For the symbology you can create a simple Arcade expression as you showed:
This will allow us to view the legend in °F:
For the pop-up you need to create the expression:
... and then reference it in the pop-up configuration (sorry for the Spanish interfaces):
As a result the information will display in °F:
Unfortunately, this is not available for the tiled service you want to use.
CC Kelly Gerrow, is this in the product plan?