Now I haven't come across an email for J-->F upgrade offer, I have noted in a post that the T&Cs make sound like it could be possible:
"
- Chauffeur-drive service is not applicable to flights upgraded from Economy Class to Business Class with this offer.
- Where upgrades from Business Class to First Class are purchased, individuals will be eligible for the Chauffeur-drive service offered for the original Business Class ticket purchased." Post 106 Upgrade emails offers FAQ
I would be inclined to say it may be possible that an upgrade email does occur although not frequently. I was planning on waiting on the upgrade email for my last trip but for completely certainty opted to pay the £300 (over and above the email upgrade price) to secure my J seat, miles and lounge access.