On an ECG (EKG) machine, in a normal Sinus rhythum (with well distinguished T waves), the interval between the start of the QRS complex and the end of the T wave, (i.e. QT interval), can be estimated as given in this wikipedia article.
Some of the issues in the measurement of QT interval are nicely summarized in this paper. The article talks about estimation in the presence of U waves, but does not mention about the problems of QT measurement when TP overlap is present.
An example of an ECG(EKG) where TP are overlapping can be seen here. It is mentioned in this context here that -
... analysis of PR intervals during exercise and recovery has been rarely addressed to date. The main reason is that the estimation of these intervals is particularly difficult at high heart rates because T wave tends to overlap the P one, which biases P wave occurrence detection (see Fig. 1)
Apart from exercise, the heart rate would also be high in tachycardia and similar TP overlap may be expected. If PR interval estimation can be difficult in the presence of TP overlap, one would expect the same difficulty for QT estimation.
How is the QT interval estimated by the machine software when there is an overlap between the T wave of the current cycle and the P wave of the next cycle? If the answer can be too involved to explain here, it would be sufficient if literature references discussing this are given. Note, the question is about measurement/estimation of QT and not about estimation of QTc.