If nothing else, the ban has revealed him for the opportunistic bandwagon-jumper he is, so with any luck...yes...it will affect his chances of electoral success.
His chances of becoming Prime Minister rest first with the British voter. Any ban from the White House has no power to affect how people in the UK vote.
He hasn't been 'banned', just advised that he won't be welcome. Anyone who doesn't approve of the Blair-Bush relationship may find sympathy with Mr Howard, but this may not extend to voting for his Party. As previously stated, it is unlikely to have a signficant effect on his political chances - people vote for what a Party will do here, not where their Leader can't go elsewhere.