My client has an online store that we are building with 10 or so products. They will also have a high street store which sells the exact same products.
It's totally possible. However, since there is no existing plugins for this that is readily available, you'd have to create a custom plugin to do it.
If you have the necessary coding chops, you can get a flying start by generating the boilerplate over at pluginfactory.io.
If not, you can hire a programmer in the Craft community to do this for you. Posting in the Craft slack channel #jobs should get you started.