Hi Mike, yes they normally do.
If you go into the Shopping Centre in Leith (Ocean Terminal) and up to the 2nd floor where the restaurants are there is an open air walkway that runs alongside so you should be looking slightly down on her as she should be moored to the left with Britannia on the right as you come out onto the walkway.
If you want to get photo's of any merchant ships then I think the 2nd or 3rd floor of the Multi story car park looks down onto the active commercial area (if you using public transport you can still get up into the car park no problem).
Your other alternative is to head for an ASDA superstore on Sandpiper Drive - Postcode EH6 6NX and that is on the opposite side of the dock looking East towards the Ocean Terminal. There were some laid-up Offshore vessels there last time I was down so that could be your landmark when looking west from the terminal - although I'm not 100% they still there. -
see photo http://www.shipspotting.com/photos/middle/4/2/8/2550824.jpg
Good luck - not the best time to be in Edinburgh as the festival is about to kick off so expect crowds and heavy rain!!!!
But enjoy anyway.
(exiled Londoner living in the Far North of Scotland!)