I've given the wrong impression by saying time will freeze. Physical time won't actually freeze. If the illusion could end, then yes, time will go on.
It's not an assumption. It is pure definition logic and logical consequence. It's an eternal illusion. If you perceive that you are forever experiencing the illusion, then that is your experience for the rest of eternity. You will forever be thinking that time is going on forever. Time will not move on because your physical self never gets to come into play. If the illusion was that your perception of time is altered but your body continues to live on, then the genjutsu/Tsukuyomi would END, and if it ENDED, it would by DEFINITION and LOGIC, be NOT CALLED INFINITE TSUKUYOMI. It would not be an infinite tsukuyomi! It would be a "very very very very long-lasting Tsukuyomi", a much more extended version of Itachi's Tsukuyomi. Because it is INFINITE, it is more than a much more extended version of Itachi's Tsukuyomi, it is THE MOST furthest extension of Itachi's Tsukuyomi. An extension that NEVER ends.
To better illustrate it, when you hallucinate, your experience really is what you experience even if the reality is. That is why it can never be wrong to say "I experienced flying pigs" because that really is what you experienced, even though it is wrong that "There really were flying pigs." Your mental story of experiencing flying pigs is 100% true. As a physical story of pigs actually flying it is false. In the same way, "I experienced time/this genjutsu go on forever in my mind" is definite. The mental story of experiencing time go on forever in your mind is 100% true. As a physical story, it is false. Your physical self did not have time go on forever.
Now for this to be literally true, your experience of time cannot EVER end. If it does, then it is FALSE that you experienced time go on forever. Since your mental experience of time can never end, for this experience to actually happen, your physical reality of time not going on forever can never come into play or else it can STOP the mental experience of time going on forever, and if it does stop the mental experience of time going on forever, then it is NOT AN ETERNAL GENJUTSU! It is NOT Infinite Tsukuyomi! It is merely "Very very long-lasting Tsukuyomi." This is just a basic principle of non-contradiction.
If you believe the physical will continue, then you basically believe that the Infinite Tsukuyomi will not happen at all or be infinite. You basically believe there is no Infinite Tsukuyomi jutsu at all; just the normal Tsukuyomi extended beyond normal limits but still within the finite confines of the original Tsukuyomi jutsu, meaning that you believe that accomplishing the experience the genjutsu is intended to effect is impossible, and that the genjutsu will end and fail to fulfil its definition of being infinite. If that is the case, you're not actually talking about an Infinite Tsukuyomi at all, you're talking about a different jutsu - Extended Tsukuyomi.
Infinite Tsukuyomi is meant to be the sure-fire way of doing something Itachi and lots of sharingan users have talked about doing for a long time but have never achieved; turning illusion into reality.
Now, if the genjutsu is disrupted, then the mind will not experience time going on forever and the physical temporality can continue. But a successful, undisrupted genjutsu, for it to reach its intention or hope to, has to have within its very nature, the power of making the mental experience time forever, which as a consequence for it to compatibly actually work, would have to prevent the physical time from going on.