ing window that gets sun from dawn to around 11 and light from then until around 5-6. Is this a system that will work?

As a general rule? No it won't work. The plants will be very leggy with very long inter-node lengths and weak stems which results in poor circulatory systems.

You simply cannot supply sufficient light for most any plants using window light only. Not only isn't the duration not long enough that time of year but neither is the light intensity nor the spectrum.

Many have tried it and most have failed. If you don't want to use lights then you'd have much better results by waiting until you can direct seed them outside. Your choice.

Dave

Thanks, Dave,
Shirley!

If you had a south exposure (or possibly a west), you could maybe pull it off. But yes, typically you grow wax begonias in a green house in winter in full sun.

typically you grow wax begonias in a green house in winter in full sun

Agree but during the winter we still have to use supplemental lighting in our greenhouse to insure full spectrum and intensity.

And we are substantially further south than the OP and have more hours of exposure and somewhat greater spectrum intensity.

Dave

Dave is spot on, and begonias are not for the inexperienced grower either. They can be extremely slow to germinate. I'm assuming TUBEROUS begonias because Shirley said they were for hanging baskets. Heck, even in our greenhouses with high tech growing systems, it takes us 8-10 weeks just to get them to transplantable size, then an additional 11 weeks to finish a basket.

I missed the clue for tuberous then...I assumed the easier wax :)

Shirley,
I grow them every year. Instead of starting in the greenhouse I begin indoors under lights so that I can monitor them. They are not difficult to germinate but as soon as they do you have to get them in good light quickly.
Don't be in a hurry to pot them on. They grow very slowly for the first six weeks and if they don't get the required light they just disappear. Keep them close to the source. Once they get past the tortoise stage I move mine into the greenhouse, but they should be fine indoors too if you have room to grow them on.