[michaf]

If the number of tests administered is the limiting factor, and if you only increase the number of tests linearly in time, then case numbers would grow linear as well.

[corpMaverick]

I suppose that in that case you would see an increase of deaths and also the count of respiratory illnesses(covid-19 missclassified).

[rolph]

yes and this would give you an opportunity to estimate how far off the mark you might be.

[unishark]

Only if all tests are positive already. Otherwise you should see an exponentially increasing number of positives if the number of infected is increasing faster than the number of tests.