TL;DR
If they develop a civilisation then yes, time will at some point become quantizied and that will be a major breakthrough in the civilisation. If they don't, then most probably not.
No civilisation
Let's face it. There are sentient animals other than humans on Earth. Currently the science claims most if not all vertebrates present some level of sentience. Yet, they have no idea of time.
Pets do not know how much time actually passed. Your dog will greet you as if you were away forever regardless if you have left for 10 minutes, for an hour or for a whole day. They may be aware of something being very long (e.g. someone is away for weeks or months where they normally are there most of the time or daily).
So if a non-civilised species on a heavily cyclic planet like that doesn't have any concept of time we can safely assume the safe to be true for any species anywhere in the Universe. Even if animals can synchronise it is due to instincts, not a concept of time.
Civilised species
From now on let me give your species a name of "nontemporians".
The situation is entirely different when we speak about developing a civilisation.
Assumptions
Just to make sure I have the right understanding of the question, let me first list some assumptions I take here.
1. All laws of physics are the same, i.e. this is ours Universe, just nontemporians has no cycles natural to them to refer to. In other words all cycles of physics, including a cycle of planet going round its star, cycle of pendulum, half-lives of chemical substances, resonating cycles of crystals and so on all remain the same. The same is about the speeds, particularly speed of light and speed of sound are constant (even though a speed of sound in the local atmosphere may be different than that on Earth). Also all other laws apply so two object dropped from the same height to which atmospheric drag has dismiss-able effect will fall on the ground at the same moment.
2. The nontemporians may not be interested in the amount of time but are aware and have the same perception of things being in the past, now or future. They can also relate to two things in the past and claim if they occurred simultaneously or not and if not, which one was earlier. In other words they are aware of something we would call a timeline of events. It might be though that they can't (at least initially) compare timelines of two different beings. On the other hand if they find a common point in the two timelines, they are aware that things before that point on both timelines happened before anything that happened after that point on any of the timelines.
3. Nontemporians are social, i.e. they value having social interactions with other members of its own species. 350
Note, I don't think a civilisation can develop without that. I assume there is a direct dependency between civilisation and sapience (i.e. you can't have one without the other). Of course I assume
Why
Sapience comes with curiosity. Species has to be curious in order to look for improvements rather than just accepting what the nature offers them. Sooner or later sapient species will try to explain things surrounding them and at some point hey will notice some dependencies. This way at some point of science development quantifiable time will become a theory that helps explain many things. As you have correctly noticed many discoveries require time in their understanding so discovery of time will be a real breakthrough.
How can I be certain? Let's look at thing that is as vague to us time to nontemporians: energy. We were exposed to energy since ever but we had no ways to measure it or quantify it. And actually it wasn't really needed. It was enough that you need to heat something more in order to change it from as solid to liquid. How much more - wasn't really important. Only with more and more theories it turned out that energy is everywhere and it sort of surrounds us, fills us and fuels us. Most of what we observe is related to energy. Movement changing, heating, chemical reaction, electricity, gravity - everywhere energy is involved. Milestones of civilisation were mostly related to energy. Using a fire was actually controlling of releasing chemical energy stored in coal (in various forms). Building a wheel was reducing energy required to move objects. When we (as a humanity) started understanding that, we were able to make most of the breakthroughs in the science.
At some point scientists started observing energy transmissions. They have noticed that the energy produced in one process can be used to fuel another process that requires energy. This led to things like engines but also to a definition off energy units - Joules and HPs.
We've been always using energy, eating, protecting ourselves from cold etc. 781