I'm a bit surprised by the replies of my learned colleagues.
I would say it does not imply that he has no current bicycle/s. And if he does have a bike currently, then it is, by definition, one of the ones he has had in this lifetime.
A: I like your new bicycle. Is this your first?
B: No, I've had several bicycles in my lifetime. [and this is one of them]
This is the present perfect, which is used for events etc. that are still true in the present.
"I've had three wives." Am I currently married? We can't tell.
But, as usual, people don't talk in isolated, cryptic sentences.