No. No no no no no.
Snape always gets mistyped as an INTJ, but literally everything is does is based on his feeelwings. He's melodramatic and irrational. In addition, he also has zero internal moral code. An INTJ may have a screwed up code, yeah, but at least they have one, whereas Snape is constantly flitting between the sides.
He comes off as an INTJ, Enneagram 4w5 {sp/sx}, to me.
It wasn't until the HBP that the readers are introduced to his pre-Death Eater life.
...The irony of burying one's tortured emotions is that it stimulates more irrational and erratic behaviors.
Snape has never gotten the opportunity to safely process and accept his experiences, which further leads him to perceive the external world as an "imminent threat" to his psychological well-being. Just as he did in his youth. Therefore, he is VERY prone to over-reacting against harmless Gryffindor student behaviors -- they serve as stark reminders of his troubled childhood.
Then Dumbledore requested Snape's services as a
double agent.
While his position was critical for the protection of Harry Potter, at a personal level, this role imposed a heavier toll on Snape's emotional health and personal development. He is further pushed into social
isolation, as The Order & Hogwarts staff continue to treat him with suspicion or downright mistrust.
"Course Dumbledore trusts you," growled Moody. "He’s a trusting man, isn’t he? Believes in second chances. But me — I say there are spots that don’t come off, Snape. Spots that never come off, d’you know what I mean?"
Ultimately, it is
extremely difficult to readjust one's jaded worldview when there is
limited outside support. There is no one to
constructively challenge your views, or the nourishment of someone who deeply cares about your well-being. Sirius had Harry & co., and many others. So did Remus.
But Snape only has Dumbledore.
Even then, their relationship is more professional than friendly. Out of necessity. For all those years, where the average person could eventually move beyond their disruptive past, Snape could not. His responsibility as a
double agent forced him to cut back on all opportunities to heal and save himself. Snape had only himself to rely on, and he hasn't learned the proper skills of managing his core needs.
When Harry said Snape was the "bravest man" he ever knew, this was probably the reason why. Most people would not be able to withstand this lifestyle, and yet... Snape was able to diligently carry out the most important mission for years without fail. His "flip-flopping" is deliberate, and executed with extreme precision. But his continuous, bully-like hostility towards the others is likely a calculated risk that Dumbledore has long accepted.
"Albus Dumbledore: "I prefer not to put all my secrets in one basket, particularly not a basket that spends so much time dangling on the arm of Lord Voldemort."
Snape: "Which I do on your orders!"
Albus Dumbledore: "And you do it extremely well. Do not think that I underestimate the constant danger in which you place yourself, Severus. To give Voldemort what appears to be valuable information while withholding the essentials is a job I would entrust to nobody but you."
— Dumbledore and Snape on the latter's espionage
In essence, as with Sirius {who was imprisoned at a young age}, the two men are both unfortunately
stuck in their Hogwarts days.
While Snape remains a tortured man with toxic behaviors, he is also loyal and committed to causes he believes in.
Of course... this
doesn't justify his toxic behaviors. But it does explain why Snape has a
hell of a time moving past the melodrama. Should he be allowed to live an ordinary life, with a group of healthy-minded friends, ...the events may turn out differently for him.
Yet... would Snape ever seize this opportunity to become a better man? Would he ever alter the pettiness? That remains to be determined.
- JK Rowling has once mentioned --
"Snape is all grey. You can't make him a saint: he was vindictive & bullying. You can't make him a devil: he died to save the wizarding world."
However, regardless of MBTI type, most people wouldn't be able to easily extricate themselves from the level of repression that Snape experienced. Whether it is self-imposed or an environmental factor. This would take
serious skill, support, motivation & dedication towards adopting healthy mindsets. Neither of which, Snape possessed before he accepted the double-agent role.
Anyway, this is just my perspective of Snape's background.
TL;DR --
My theory is that in "ordinary" circumstances, Snape would still retain those vindictive and bullying
tendencies, but he wouldn't be such an irrational, melodramatic nutcase about it. That is more of a side-effect of his repression.
And determining the MBTI type on the *presence* of emotional stability isn't very effective. We all posses the capacity for unhealthy tendencies, except each individual may go about it in a
different manner.