Everything is possible. But first consider if you actually need to write your own app, or you prefer just to use existing tools (see the comment under your answer).
If you choose to use Google maps for georeferencing - then the question is:
- Is the image in a projection compatible with Mercator Projection EPSG:3857 (this is used by google maps)?
- Is the image oriented correctly, i.e. no need for rotation?
If you answer NO to any of these questions, then you will have problems in Google maps - you will have to reshape the image yourself somehow, because google maps cannot do this by default.
However, if the answer is YES to both questions, it is quite simple. In Google maps, you have several options how to put image over the maps.You can use Ground overlays or Custom overlays from Google maps API v3 - there is a very good documentation with examples (ground overlay, custom overlay). Ground overlays seem to be simpler, you just put an image over the map and specify corner coordinates. Custom overlays allow for more functionality, but are more complex to use.
Or you can create layer tiles and use
google.maps.ImageMapType interface. But for smaller images I think the ground/custom overlays are much simpler solution.