Can academic teaching and quality research go hand-in-hand? [Long]

I have been working in a very well known university in India. I am a faculty member in the department of Computer Science. My appointment to the university is somewhat temporary given the condition I have to finish my PhD within x-years (Please ignore x for the time). If I can not finish my PhD within this duration, I have to leave the job and/or PhD.

Given the following conditions, you could see that it is difficult.


This is one of the premier and oldest university in India which is very well known for its quality teaching.
The university also expects top quality research for acceptance of the PhD thesis.
All the faculties of the same level as mine, are one of the back-bone of the department(s) of the university.
All the faculties must contribute towards institutional development in addition to quality teaching and research/PhD.


I can understand that this is a good sign that we can learn teaching/research with time. However, for me it seems very tough. I have been planning for a full-time PhD somewhere abroad with a stipend. However, I am tensed about future opportunities post PhD.

I understand that PhD students are given some amount of teaching load as a part of stipend policy. But, this academic teaching load is really incomparable and is too high.

Considering above facts, how to manage these two things together?

[Short]

Can academic teaching and quality research go hand-in-hand given a time-bound on job?

P.S. I belong to computer science and mathematics community and an independent scholar. Research is my passion.

[Edits]


There are two different courses (full course) assigned each with a student strength of 100 (approx.).
The courses involve labs as well.
So, in every 1.5 day, you could assume to have a class for which you need to plan your day properly (such as preparing materials, teaching slides, assignments, lab assignments, surprise tests if any, and few other things)


The point of writing I have been planning for a full-time PhD somewhere abroad with a stipend. is to get advises from experienced persons here on Academia.SE on whether should I go for it or not.
Sure, this is exactly what is expected of tenure track faculty at research intensive universities in the US. It is a lot easier when you have a little teaching experience and a little research experience before diving into the "deep" end, but there is no reason teaching and research cannot go together. In the US a PhD student might be expect to teach a single class in both the fall and spring semesters while a tenure track faculty might be expected to teach 3 classes each semester.