NS,
Depends when he means by “rapid” and when he thinks the “rapid expansion” occurred. It was rapid after Constantine (unsurprisingly), but how rapid it was before then compared with other faiths is debatable.
Don't think events 280 years after the supposed resurrection can be considered rapid. As already covered, it's a vague claim but in the absence of any details, it's only reasonable to apply normal usage.
Given he's also cited persecution, then after Constantine can't apply. Doubly so, since he's ruled out spreading through conquest. I think we probably agree that the claim isn't defined in any level but is not much more than a mantra rolled out without thought.