Your question drives at the definition of "true randomness", which is a deep question and not altogether resolved. But in short, in modern physics we believe the answer is yes. Indeed there is a whole body of knowledge around Bell's Theorem and the untenability of notions of countefactual reality (the notion that the outcome of a quantum measurement exists before the measurement is made), so we believe in principle that we cannot foretell in any way exactly when a radioactive decay event will happen.
Many philosophers and mathematicians who deal with foundational questions about notions of randomness and probability theory go even further than this: they look to modern quantum mechanics as a model for what randomness truly is and for help in formulating notions and definitions of randomness. You can get a feel for thisfrom the Stanford Encyclopedia of Philosophy a most excellent resource, particularly under the pages:
Chance versus Randomness
Interpretations of Probability; and
You'll quickly see that rigorous underpinnings of propability and statistics are a work in progress.
One definition of true randomness can be the following. Can we foretell the times at which decays will happen such that there is any nonzero correlation between the observed and theoretical times? If the answer is no then the sequence is random. One can define this notion more rigorously through Kolmogorov Complexity. Thus, informally, we talk about randomness as futility of foresight: we can have no foresight into true randomeness.
So you have a whole sequence of numbers encoding the time differences between successive events at your radiation decay detector. We don't believe, on average there is any way of describing this sequence that is a shorter description than simply naming the time difference timeseries itself: the mean ratio of the complexity $K(X)$ of the observed sequence $X$ to the length $L(X)$ of the raw sequence approaches unity as the sequence length approaches infinity.