We know that in 1994, the Triwizard Tournament was hosted by Hogwarts and the inter-House Quidditch Cup did not take place as a result of this. My question is, when Hogwarts hosted the Tournament all those other times, did they cancel the Quidditch Cup?
This is not canonical.
The Tri-Wizard tournament was established in 1294, and in that time, a tournament would occur every five years, with each house hosting it in order. However, the tournament was closed down due to an issue in 1792. Other than this, we do not know of any other times in which this happened. According to the HP Wiki (which I dare say can be very unreliable at times), the tournament has occurred at least 125 times. For some reason my math appears to be wrong on this one, but let's just go with the Wiki.
125/3 (one school per 5 years - held at Hogwarts every 15 years) = 41~ (times held at Hogwarts)
Now, as the Triwizard tournament only occurs every fifteen years at Hogwarts, it can be assumed that it takes priority over any event at Hogwarts due to the importance of the former.
As you can see, it was only hosted at the school forty one times (if my math is correct), which shows the significance and priority of the tournament. Forty one compared to every single year that the Cup is awarded, is a great deal of importance.
No specific proof about it in the books.
But, a fair assumption would be: Yes, they did cancel the Quidditch Cup whenever they hosted the Tri-Wizard tournament, if the dates collide. (Else, they'd shift it forward or later, but a sensible option would be to cancel altogether in order to not let the acads suffer)
It's like the Intra- and Inter- sports tournaments at every institute. The schools take the Tri-Wizard tournament very prestigiously.
In addition, having two tournaments in a year takes a huge toll on the academics both costing time and efforts.