Yes, training legs absolutely increases testosterone levels, as does working any other muscle; whether it be chest, triceps, biceps or back. What then makes squats so special? Well, the amount of testosterone, growth hormone, or IGF-1 released during workouts is directly related to how much muscle mass is stimulated. Therefore, performing compound movements that work larger muscle groups, recruiting more motor units creates an anabolic environment which is superior to the anabolism that results from isolation work on smaller muscles. 
There is nothing inherently “magical” about exercises like squats or dead-lifts other than the facts that they are extremely challenging, involve larger muscles, and recruit more motor units from other parts of the body to assist with balance and stability.
Sounds great, right? Well, there are a few caveats that must be observed to ensure optimal anabolism…
How Doing Squats Increases Testosterone Levels
The squat is known as the king of exercises for good reason; squats are said to involve 300+ muscles by most estimations. The greater the degree to which any exercise involves the rest of the body, the greater the degree to which hormones like testosterone, growth hormone & IGF-1 are released.
Follow these training guidelines for the best results:
Reps: The classic hypertrophy rep-range used by bodybuilders (8-12 reps) produces vastly superior testosterone levels compared to power (3-6) & strength (1-5) rep-ranges. 
FYI: It should be noted that intensity is key. You need to be working hard for those 8-12 reps; bodyweight squats aren’t going to create a Hulk-worthy environment of anabolism. Sorry. 😞
Now, about that testosterone…
Does Testosterone Grow Muscle?
Exactly how big of a deal is all this extra testosterone, really?! The thing about this exercise-induced testosterone spike is that it is acute (short lived) with hormone levels returning to baseline at about 60 minutes post workout. So, it seems that the increased muscle hypertrophy that results from following this training protocol is not technically driven by the increased testosterone, per se.
Rather, it seems that the stressing of greater amounts of motor units during these very demanding compound movements leads to increased muscle protein synthesis (MPS) which more directly drives this increased hypertrophy.
This is what I’m getting at:
Or as the researchers so eloquently put it:
“Four hours post training MPS increased 50% above baseline and increased to 109% (nearly double) at 24 hours. At approximately 36 hours, MPS had returned to 14% of baseline (i.e., the control arm). This study suggests that following a heavy bout of resistance exercise MPS more than doubles by 24 hours, then rapidly declines to baseline around the 36-hour mark. MPS will be elevated for a maximum of only 36 hours. This begins to question the recovery timeline, and the old school mentality of waiting seven days to train the same muscle again.” 
Getting to the practical application part of this article we come to the sneaky little question that has probably been on everybody’s minds: Will working legs help upper body?
How Squats Make Your Arms Bigger
Norwegian researchers discovered that the secret to bigger biceps gains is to workout legs immediately before getting into arm training. Those who blasted out squats prior to training biceps saw greater arm gains than those who skipped this miniaturized version of leg day. 
So, by using heavy compound leg exercises as a means of quickly flooding the body with high levels of anabolic hormones prior to curling, biceps saw greater gains. It then stands to reason that if this methodology works for biceps, the same should hold true for triceps, chest, back & shoulders. In other words, training legs will help with your non-leg training; so, make better upper-body gains by working legs first.
Almost twenty years ago I can remember seeing a headline on one of the popular muscle magazines which stated something to the effect of, “you don’t get big arms from doing curls…” Having grabbed my attention, I eagerly navigated my way to the full article and got to the 2nd half of that statement & the punchline, “…you get big arms by getting bigger all over.” (maybe “punchline” wasn’t the best choice of words, because the knowledge received that day (though “bro-science”) was no joke!
“But Won’t All Those Squats Make My Legs Sore?!” 🎻😭
Yes, initially… but the more often you do them, the less severe the DOMS will be.
The principle of specificity is more commonly known as the SAID principle, which stands for "Specific Adaptation to Imposed Demands." The SAID principle asserts that the body will adapt to the specific demands placed upon it. Specificity training implies that you must practice a skill in order to get better at it. In other words, you get what you train for.
Intelligent Lower Body Programming
Let me ask a question: How many days a week do you train upper body?
Follow up question: Is everyday an arm day, or chest day? Don’t you split your workouts into push/pull, chest/triceps, back biceps? Or maybe you have arm day, shoulder day, chest day, etc.?
What I’m hinting at is this: it would be smart to split up your lower body work like you do for your upper body. Perhaps one day can be a quad-dominant squat day, followed by a hips & hamstring-dominated dead-lift day.
The secret is out: You get bigger biceps from working legs, not from hammer curls.
Nobody ever said it would be easy, but if there’s a method to your madness you can ensure insane gains for 2020 and beyond!