Depends on the begonia and the amount of shade you are talking about. Some begonias will do well in shade but may not bloom while others will simply fade away and die. Only way to find out is try it.

So I take it most 'garden variety' (semperflorens) begonia require more sun than a shade impatiens?

Lots of people put semps in full sun in our area (Atlanta) which is usually a big mistake because they bake in the hot, dry sun - maybe if they were watered daily they'd do okay. Too much shade though may grow the biggest leaves but I don't know how the blooms would be. If you have dappled sunlight then they should do great.

Are you talking about Wax Begonias? Leaves are green or purple?
They thrive in full sun. In fact, they need the very brightest light bloom. They'll do okay in shade, but can grow spindly, and might not flower as fluently if in too shady a spot.

When I plant Wax Begonias in front, they get direct west, south and north light. Toni

I d on't know of any purple leaf wax begonias - maybe bronze leaf.

In the south you don't want to plant wax begonias in full sun - lots of folks do, but they eventually look like crap. Maybe in the north they can be planted in full sun without a lot of fanfare. Maybe if they kept them watered every other day then they would look good but most look like they need to be yanked out and replaced with something else by mid June.