end of Terminator Zero season 1 doesn't necessarily mean he won't return in future, and if he does, his ingenuity has proven he could be an even bigger threat than he already has been.
The logic provided by the show regarding Terminator Zero's timelines strongly suggests that the animated project exists within its own continuity while also remaining relevant in the larger franchise canon. As such, while Olyphant's Terminator could technically meet a T-800 that looks like Arnold Schwarzenegger, there's no guarantee it would be exactly the same version of the character(s) from the first two movies. However, that could be a blessing in disguise, as Olyphant's cyborg has already established himself as superior in one key way.
The Terminator's Arm-Mounted Crossbow Is A Brilliant Addition To The T-800
Schwarzenegger's Terminator character had to find his own weapons
There's no denying that Schwarzenegger's T-800 is a terrifying specimen, especially when he's playing the bad guy in the first movie. He's stronger, faster, and more durable than the humans he's programmed to kill, but Terminator Zero takes Skynet's almost unstoppable design one step further. Not only does Olyphant's T-800 have a crossbow integrated into his forearm, but he also has the creativity and initiative to fit it himself using salvaged components from the 20th century. On the other hand, Schwarzenegger's T-800 lacked any conventional weaponry.
Terminator Zero's bad guy having space for a crossbow in his arm begs the question of why all T-800s don't have them fitted under the flesh so they can bring them back from the future.
Although Terminator Zero never implicitly states the story's bad guy is also a T-800 like Schwarzenegger's character, it's reasonable to assume he is - even if he does have a different face. So, it stands to reason that the original T-800 from the first two Terminator movies had the potential to upgrade itself but just never did. That being said, there are some very good reasons both in and outside the Terminator canon for why this could be the case. Regardless, it doesn't take away from how cool it is that Zero's T-800 would have an edge over Schwarzenegger's.
Why Arnold Schwarzenegger's T-800 Didn't Have Integrated Weaponry
Skynet may have had its reasons for withholding extra bells and whistles from Schwarzenegger's character
Most human characters who faced the original T-800 stood almost no chance of victory in a face-to-face conflict. Schwarzenegger's Terminator was already so powerful that giving him a crossbow or another projectile weapon wouldn't have made for a very entertaining story, as he would just win every standoff almost immediately. Knowing this, it was likely a conscious decision by James Cameron for him to stop adding to his death machine at a certain point. The in-universe theories, however, are far more compelling.
Olyphant's T-800 may have been provided with upgrade blueprints for if other weapons proved difficult to acquire.
One of the biggest differences between Terminator Zero and the rest of the franchise is where the anime is set. Every other previous installment has taken place in the US, whereas Zero takes place in Japan. The original T-800 being sent back to 20th-century America didn't call for integrated weaponry, as firearms were and still are easy to access. As such, Skynet may have seen the addition as superfluous. Gun control in Japan is far stricter, as shown in Terminator Zero. Therefore, Olyphant's T-800 may have been provided with upgrade blueprints for if other weapons proved difficult to acquire.
Terminator Zero Kept Its Terminator Model Design Simple & Effective
Olyphant's T-800 was only slightly upgraded
Netflix's animated Terminator project had some tough decisions to make when penning the scripts. The Terminator movies have rewritten the canon several times and added more variants of the franchise's titular cyborgs through the decades. So, the anime could have pulled from all this additional lore or simply stuck to basics. Thankfully, the latter option was made, and the result was far more effective.

Terminator Zero Season 2 Can Flip Judgment Day's Biggest Twist Thanks To Season 1's Finale
Terminator 2: Judgment Day features a huge twist that would be easy to repeat in Netflix's new anime, but the spinoff seems to have other plans.
The T-1000, as introduced in the form of Robert Patrick's character in Terminator 2: Judgement Day, was a far deadlier version of the Skynet hardware. While the T-800 was great and the upgrade was partially responsible for a thrilling storyline, a shapeshifting Terminator is also far more gimmicky than the T-800. If Netflix had used the T-1000 instead of the T-1000 for the story's villain, it would have been an entirely different show. Having said that, there is still the possibility of Terminator Zero introducing a variant like the T-1000 or beyond if the show returns for a second season.