You can use an ElementLayer to display images or videos.
There is a sample here : http://help.arcgis.com/en/webapi/silverlight/samples/start.htm#MediaLayer
Note that Silverlight doesn't support tiff format though.
So you will need either a 3rd party component or a conversion to a supported format (jpeg, png (no gif nor tiff)).
As far as I understand from the sample I will replace the
Source="http://serverapps.esri.com/media/scec-shakeout-simulation-rt.wmv"
line with the url of the imagery and I will be done , correct?
If I change the projection of the map, will this imagery also change projection?
Almost! You have also to set the esri:ElementLayer.Envelope to the correct map coordinates for your image.
Nothing automatic. You have to adapt the envelope of your element to the map coordinates.
Doing this adaptation, are there any libraries I can make use of during calculation of this transformation between projections? Or am I on my own?