Yes, static electricity can build up on an antenna, and it will give you a nasty nip if you touch it.
I have seen sparks 15mm long discharging from an antenna feeder.
This sort of thing does not happen all the time, I have only seen it during cold dry weather when it has been "snowing" little round balls of ice.
This was quite common in the Shetland Islands when I lived there several years ago, I have also seen it here but not for a long time.
As for getting any usefull power from it, not a practical proposition.
JimB