[IslandJeff]

for the last half of her life she repeatedly wrote letters questioning the existence of God

You've never been a man? A wandering organic mass of self-interest and discontent? The Apostles themselves had moments of reflection, no?

[HarleyD]

The Apostles themselves had moments of reflection, no?

I don't know anywhere in scripture that the Apostles (or any believer for that matter) doubted the existence of God. So, to answer your question, "no" is correct.