I think the chances of that happening are slim to none. This is the second son of the venerated Diana and the son of the future king. Fanfare is a given. Something on the scale of Edward and Sophie's wedding, maybe, but to expect the public to be satisfied with some pictures of them going in and out of a small church is not going to happen.
They're low-key and protective of their privacy because they have to be. W&K were the same in their dating days, it's what's expected. If they were out flaunting themselves for the paps every day the naysayers would have a field day.
Harry is first and foremost son of the heir to the throne and grandson to Elizabeth II, the most popular/iconic head of state (many will say person) in the world.
And as I've written in previous posts in this and another thread:
Princess Elizabeth 1947: To and from Westminster Abbey in closed carriages and appearance on the balcony.
Margaret 1960: To and from Westminster Abbey in closed carriages and appearance on the balcony. (That had not happened today)
Anne 1973: To and from Westminster Abbey in closed carriages and appearance on the balcony. (That had not happened today)
Charles 1981: To and from St Paul's Cathedral in open carriages and appearance on the balcony.
Andrew 1986: To and from Westminster Abbey in open carriages and appearance on the balcony. (That had not happened today)
Edward 1999: A big televised Royal Wedding at St George's Chapel with a carriage procession in Windsor.
William 2011: A scaled-down wedding in comparison with the Abbey weddings mentioned above.
To Westminster Abbey in cars and back to the palace in open carriages for William/Kate and the bridal party, and closed carriages for the Queen/Philip, Charles/Camilla and Kate's parents and appearance on the balcony.
A possible wedding for Harry:
The monarchy is as popular as ever with record high support in several polls since 2002, some of over 80%, but we live in a different era with a more critical press than we did in the 60s, 70s and 80s.
And remember: William is the eldest son of the heir, and he was as popular as Harry (if not even more) when he married, and there were still complaining from media and other people about the costs etc.
I'll therefor be very surprised if he gets a Abbey wedding with a carriage procession and a balcony apperance.
I think we'll see much of the same as we saw for Edward in 1999, A big Televised Royal Wedding at St George's Chapel with a carriage procession in Windsor.