Yes, it is possible, but is not common in everyday speech. "Testings" is more used in formal literature, like scientific or engineering journals.
Intercorrelations of all testings of all tests were run, in order to determine the relationship of the various tests to each other.
The following tables give the customary summary of the results of the testings ... of the quality of the gas supplied by the three Metropolitan Gas Companies.
In statistical academia, the issue of multiplicity is also known as the problem of multiple testings or multiple comparisons.
One exception is in certain discussions of Christian thought, in which "testings" refers to the trials of Jesus Christ in the New Testament:
It would be better to speak of testings rather than temptations, since the latter word has too often become associated with a yielding approach which was certainly not present in the case of Jesus.
In everyday speech, use tests.
I am awaiting the results of the genetic tests.