Switching to Stream from satellite service - what happens to the programs I recorded on the satellite box?

Yes, you would lose your DVR recordings.  Even though they are both Directv they are 2 different services.

You can keep your satellite service until you've watched any valuable recordings. It's easy to have both services. Just use a different email address for your new DirecTV Stream account. That's what I did for a couple of months while I finished watching stuff on my satellite DVRs. 

I believe they are gone. They are in the box, but you cannot play them. I disconnected my cable box when I went to DTV stream. All recordings are lost. 
the only good thing is, now you have cloud DVR, and you won't lose them. However, DTV auto deletes them after about 9 months. 
I am not pleased with this service, not for $90 a month. But my husband likes it. When he is gone, DTV will go with him. 
he is dying and I try to keep him happy. 

You can’t play them because the access card is no longer active and thus doesn’t have DVR service. The recordings don’t just ‘disappear.’

Think of it as turning off your computer and turning it back on a few hours later. The data doesn’t just disappear, granted you don’t delete it of course.

DirectTV streaming TV guide channel numbers are not bright and are difficult to see from the couch.