All things being equal** you'll actually make better strength and size gains in your upper body if you don't train legs. Leg training burns up a ton of calories, burns up a ton of nervous system energy, and requires a lot of adaptive resources. You only have so much to go around.
Same goes for cardio, HIT etc. Anything that burns calories and requires energy takes away adaptive resources that could be used to fuel strength and size gains.
As a personal example, when I was 23 I experiencing bouts of rapid and irregular heartbeats and for 2 months I couldn't train legs. I kept doing the same upper body workouts I'd been doing before but they were a lot more effective simply because I didn't have legs to worry about. I made more upper body strength gains in that 2 months then I had in the previous year and a half combined. The workouts were exactly the same as before, they just worked a lot better.
**Here's the thing though: Things are rarely equal. Most people don't train their lower body hard enough to impact recovery. One lower body workout a week certainly isn't gonna do that. People that train legs (and whole body lifts like deadlifts) are usually more dedicated and have their shit together. They're more likely to have a good diet and much more likely to be consistent about their training. Thus, they make better gains everywhere in the long term because it's more important to them. The average frat bro might put more on his bench and curl in the few weeks he's prepping for spring break, but in the long term the guy doing the full body lifts will win out simply because he's doing more things right and it's more important to him.
The hormonal effect of full body lifts really isnt' worth getting worked up about from an anabolic perspective. From a catabolic (fat-burning) perspective it cetainly is. Full body/lower body lifts burn a lot more calories and can drastically increase things like AMPK and GH. If you're looking to stay lean their is a big differnce, but for size and strength those things are actually a disadvantage.